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A    NEW    TREATISE 


STEAM    ENGINEERING 


PHYSICAL   PROPERTIES  OF  PERMANENT   GASES 


DIFFERENT  KINDS  OF  VAPOR 


BY 

JOHN  W.   NYSTROM,  C.  E. 


NEW   YORK 

G.    P.    PUTNAM'S    SONS 

182    FIFTH    AVENUE 


Entered  according  to  Act  of  Congress,  in  the  year  1876  by 

JOHN  W.  NYSTROM, 
In  the  office  of  the  Librarian  of  Congress,  at  Washington. 


Eagineerng 

Library 

TJ 


PREFACE. 


THE  object  of  this  treatise  is  to  furnish  a  variety  of  matters  pertain- 
ing to  STEAM  ENGINEERING  which  appear  to  be  wanting  in  that  pro- 
fession, and  which  have  heretofore  not  been  published. 

The  authors  consulted  for  this  work  are  eminent  experimenters, 
such  as  Regnault  and  Rudberg  on  steam  and  gases,  Faraday,  Pelouze 
a*nd  Andrews  on  carbonic  acid,  Favre  and  Silberman  on  heat  of  com- 
bustion, Kopp  on  volume  of  water,  Fairbairn  and  Tate  on  volume  of 
steam.  None  of  these  savans,  however,  are  responsible  for  the  formu- 
las and  tables  herein  deduced  from  their  experiments. 

Where  physical  sciences  are  not  sufficiently  developed  to  establish 
a  law  of  action  mathematically,  experiments  are  made  for  the  purpose 
of  guiding  us  to  the  law ;  but  it  can  rarely  ever  be  expected  that  ex- 
periments alone  can  give  perfect  results,  but  they  give  an  approxima- 
tion to  the  law  of  variation,  which  must  finally  be  adjusted  and  estab- 
^  lished  by  the  aid  of  mathematics.  This  is  what  has  been  attempted 
s  in  the  present  work. 

It  was  at  first  not  intended  to  include  in  this  work  the  steam-tables 
.^  which  are  published  in  the  author's  Pocket-Book,  but  after  having 
^  carefully  investigated  the  Fairbairn  experiments  and  formula  for  vol- 
ume of  steam  and  concluding  that  they  could  not  be  relied  upon,  it 
\  was  therefore  decided  to  calculate  new  steam-tables  and  extend  them 
to  a  pressure  of  1000  pounds  to  the  square  inch. 

The  relation  between  temperature  and  pressure  of  steam  is  also 
slightly  altered  in  the  new  steam-tables  so  as  to  conform  to  a  uniform 
curve  or  law,  because  the  average  curve  adopted  by  Regnault  does 
not  follow  a  regular  law,  and  therefore  indicates  that  there  must  have 
been  some  inexactness  in  his  experiments. 

When  the  author  worked  out  the  first  steam-table  in  the  Navy  De- 
partment under  the  direction  of  Chief-engineer  Isherwood,  the  irreg- 
ularity of  the  Regnault  curve  was  then  demonstrated  with  attempts 

3 

733250 


PREFACE. 


to  correct  it,  but  the  Chief  would  not  allow  any  deviation  from  that 
curve.  The  difference  is,  however,  within  probable  experimental 
errors,  and  so  small  that  it  is  not  of  much  importance  in  practice. 

The  author  believes  that  the  relation  between  temperature,  pres- 
sure and  volume  of  steam,  as  given  in  these  new  tables,  is  nearest 
right.  The  old  steam-tables  are,  however,  referred  to  and  used  in  the 
body  of  this  work  for  the  reason  that  many  readers  may  have  more 
faith  in  them  than  in  the  new  tables,  which  are  equally  applicable  to 
the  examples. 

Many  mathematical  proofs  have  been  omitted  in  this  work  in  order 
to  avoid  extensive  algebraical  demonstrations,  which  are  objection- 
able to  the  general  reader  who  only  needs  the  resulting  formulas  for 
the  insertion  of  his  given  numerical  values. 

The  .principal  formulas  are  accompanied  with  examples  and  also 
tables  ranging  between  practical  limits,  showing  at  a  glance  the  rela- 
tion between  and  proportion  of  the  operating  elements. 

The  calculus  has  been  resorted  to  in  only  a  few  cases  of  necessity 
where  the  result  could  not  otherwise  be  reached. 

The  numbers  of  the  examples  are  arranged  to  correspond  with  the 
numbers  of  the  formulas,  and  therefore  do  not  run  in  order. 

Profound  and  high-sounding  terms,  like  "potential  and  kinetic 
energy,"  etc.,  are  not  used  in  this  work,  which  limits  itself  to  simple 
terms  such  "as  are  used  in  the  shop,  and  which  express  the  true  mean- 
ing of  the  respective  cases. 

The  appendix  on  "  Mechanical  Terms "  is  added  to  this  work  to 
furnish  an  idea  of  the  unsettled  condition  of  that  subject. 

Similar  discussions  have  been  published  in  pamphlet  form  and  dis- 
tributed gratis  to  institutions  of  learning. 


ALPHABETICAL  INDEX. 


A.  PAGE 

Air,  compression  and  expan- 
sion of       ...  128 
"    for  combustion        .        51, 53 
"    quantity  of,  for  draft  62 

"    work  of  compression  and 
'          expansion  .         .         .132 
Alcohol  vapor,  properties  of    164 
Ammonia  vapor    .         .         .166 
Appendix      ....  171 
Aqueous  vapor,  properties  of   139 
Atmospheric  pressure,  horse- 
power of    .        .        .        .27 
Available    heat    of   combus- 
tion  .         .         .         .51,53 

B, 

Benzine,  vapor  of          .         .165 
Boilers,  explosions         .         .82 
"       generating  steam       .     18 
"       horse-power     by     B 

and  a  .  .  37,40 
"  inspector's  rule  for  .  89 
"  lap-joint,  riveted 

92  to  105 

"  legal  horse-power  of  35 
"  plates  must  be  stamped  89 
"  standard  efficiency  of  52 
"  stays  on  flat  surfaces  108 
"  strength  and  safety 

of.        .        .      89-109 
Boiling    point    of    different 

liquids       .        .         .         .168 
Burning  of  smoke         .         .     57 


0.  PAGE 

Carbonic  acid,  properties  of  .  136 
Cause  of  boiler  explosions      .     86 
Chimneys,  general  properties 
of          ...         42,122 
"         correction     for 

height  of    .        .     41 
"         horse-power  of      .123 
Collapse,  strength  of  gue  for     106 
Combustion  of  coal  per  height 

of  chimney        .         .         .41 

Combustion,  incomplete          .     47 

heat  of      .        .     46 

power  of    .         .43 

"  products  of        .     56 

properties  of  air 

for          .        .    45 
Colors  for  tempering  steel  63 

Condenser,  fresh  water  .         .     67 
Correction  for  temperature  of 

feed-water          ...     21 
Correction  for  height  of  chim- 
ney     41 

Covering  steam-pipes     .        .81 

D. 

Distillation  of  petroleum       .  168 
Destructive   work    of   boiler 

explosions          .        .         .85 
Draft,  velocity  of,  in  chimneys 

60-122 

Draft,  natural,  in  furnaces          59 
"      temperature  of   .         .45 
"      quantity  of  air  for      .     62 
5 


ALPHABETICAL  INDEX. 


Dryness  or  humidity  of  steam  143 
Dynamical  terms  .  .  .171 
Dynamics,  principles  of  .  14 

E. 

Economy    of    heating    feed- 
water         .        .        .         .54 
Elasticity  of  permanent  gases  112 
Ether,  vapor  of     ...  165 
Equivalent  work  of  heat  in 

steam         .         .         .         .142 
Equivalent  of  heat,  dynamic      30 
Evaporation  from  and  at  212°     53 
legal  horse-pow- 
er of      .         .     40 
"          natural  effect  of      23 

per   square   foot 
of  Q          ....     66 
Expansion   and   compression 

of  air         .         .         .  129-133 
Explosion  of  steam-boilers    .  142 

F, 

Fairbairn   and   Tate,   steam- 
volume      .         .         .      19-144 
Feed-water,  heating  of  .         .54 
"          quantity  of          .     76 
reduction  for  tem- 
perature        .     22 
Feed-pump,  capacity  of         .77 
Felt  covering  for  steam-pipes     82 
Fire,  management  of    .         .55 
Fire-grate,  spaces  between     .     57 
Flues,  strength  of,  for  collapse  106 
Fresh  water  condenser  .         .57 
Fuel,  heat  generated  by         .     48 
Fuel,  properties  of  .50 

Furnace  draft,  natural  .         .     59 

G. 

Gases  in  chimney,  tempera- 
ture of  .     64 


Gases  in  chimney,  velocity  of  122 

"     permanent  .         .         .  112 

"     specific  heat  of    .         .119 

Gauge,  water,  for  draft  .         .     61 

Grate-bars,  spaces  between     .     57 

H. 

Heat,  available  by  combustion  53 
"  of  combustion  .  .  46 
"  in  water  and  steam, 

units  of  .  .  .141 
"  permanent  gases  .  .  1 20 
"  lost  by  radiation  .  78-82 
"  lost  through  chimneys  63 
"  physical  constitution  of  18 

Height  of  chimneys      .      42, 123 

Horse-power  of  steam,  natural 
of      ....        20,23 

Horse-power    of    steam-boil- 
ers   .        .        .        .       32,36 

Horse-power  of  boilers  by  E3 
and  Q  .         .        37, 40 

Horse-power  of  chimneys   42, 1 23 
"  by    volume    of 

steam     .         .     74 

Humidity  of  steam        .         .143 

Hyperbolic  logarithms  .         .     29 

I  and  J. 

Inflammation  of  petroleum  .  168 
Inspectors  for  steam-boilers  .  89 
Joints,  lap-,  for  riveted  boilers 

92-105 
K. 

Kabyl,  French  ether  ship  .  1 64 
Kerosene  .  169 


Lap-joints,   single   and   dou- 
ble riveted  92-105 


ALPHABETICAL  JXDEX. 


Lateut    heat    in   water    and 

steam  .  .  .  139-141 
Laughing-gas  .  .  .166 
Law  of  the  United  States, 

steam-boilers      .         .         .89 
Legal  horse-power  of  steam- 
boilers      .         .        .        35-40 
Letters,  standard  notation  of    10 
Locomotive  without  fire         .  110 
Logarithms,  hyperbolic          .     29 
Loss  of  heat  through  chim- 
neys .        .        .        .63 
Loss  of  heat  by  radiation     78-82 

M. 

Mean  pressure  of  steam  28, 160 

Mechanical  terms  .         .  .12 

Moisture  in  fuel    .         .  .49 

N. 

Natural  effect  of  full  steam  19,  20 
"  "       of    expanded 

steam  .  .  .  .26 
Natural  effect  of  furnace 

draft          .         .         .         .59 
Notation    of    letters,    stand- 
ard     10 

o. 

Oils  of  petroleum          .        .169 
Oxygen  and  hydrogen  in  fuel     49 

P. 

Petroleum  as  fuel .         .         .53 
"         oils,  properties  of  .  1681 

Permanent  gases   .         .         .  112  \ 

Plates  for  boilers  to  be  stamp- 
ed       89 

Power  of  combustion  .  .  43 
"  "  steam  without  fire  .  110 
"  lost  by  radiation  .  79 


PAGE 

Primary  source  of  power       .     1 7 
Products  of  combustion         .     56 
Protoxide  of  nitrogen   .         .168 
Prevention   of  boiler   explo- 
sion   86 

Q. 

Quantity  of  steam  escaping    .     72 
of  feed-water  .         .     76 

R. 

Radiation  of  heat  from  pipes  78-82 

Reduction  for  temperature  of 
feed-water  ...  22 

Reduction  for  height  of  chim- 
ney   41 

Revolutions  and  steam-pres- 
sure   74 

Riveted  lap-joints         .      92-105 

S. 

Safety-valves         .        .        71,67 
Sit  for  safety-valves       .         .     69 
Smoke,  burning  of         .         .     57 
Specific  heat  of  gases    .         .119 
Staying  of  boilers          .         .108 
Steam  engineering         .         .17 
"      engine    versus    water- 
wheel         ....     17 
Steam,  natural  effect  of          .19 
"      volume,  Fairbairn's  19,144 
"      boiler  explosions         .     82 
"      boiler  experiments      .     1 8 
"      expansion  of      .        19,  24 
"      equivalent  work  of    19,  20 
"      velocity  through  open- 
ings        .         .         .70 
"      quantity  escaping       .     72 
"      power  without  fire      .  110 
"      or  aqueous  vapor        .  139 
"      dryness  or  humidity  of  143 


ALPHABETICAL   INDEX. 


PAGE 

Steam,  superheating  of  .         .  147 
Steam-pressure    and    revolu- 
tions  74 

Stamped  boiler-plates  .  .  89 
Strength  of  boilers  .  88-109 
"  flues  for  collapse  106 
Superheating  steam  .  .  147 
Spherical  ends  of  boilers  .  162 

T. 

Technical  terms  .  .  15-170 
Tempering  steel,  colors  of  .  65 
Thermo-dynamics  .  .  30 
Temperature  of  feed-water  .  22 
Temperature  of  gases  in 

chimneys  .         .         .         .64 
Turpentine  vapor .         .         .164 

U. 

Uncombined  oxygen  and  hy- 
drogen .  .  .  .49 

United  States  law  for  steam- 
boilers  .  .  .  .89 

Units  of  heat  in  steam  and 
water  .  .  .  .141 

Units  of  heat  in  permanent 

.  120 


Units  of  heat,  definition  of   .     46 
"      of  heat  of  combustion     46 

V, 

Vapors,  different  kinds  of  .164 
Velocity  of  draft  in  furnaces  .  60 
Velocity  of  steam  through 

openings    .         .         .         .70 
Volume  of  steam,  horse-power 

by 74 

Volume,  ultimate,  of  gas       .  115 
Volume    of   water,    temper- 
ature        .         .         .         .140 
Volume  of  steam  .         .      19,144 

W. 

Water,  feed,  temperature  of  20,  22 
Water  and  steam-power  com- 
pared       .         .         .         .17 
Water-gauge  for  furnace  draft     61 
Water  volume       .         .        .140 
Work  of  steam,  natural       19,  20 
Work  of  steam-boiler  explo- 
sions         .         .         .         .85 

Z. 

Zero  of  temperature,  absolute  113 


ISDEX  TO  TABLES. 


TABLE  No.  PAGE 

1.  Reduction  for  temperature  of  feed- water       .         .         .  .22 

2.  Natural  effect  of  evaporation  of  water  in  horse-power  .  .     23 

3.  Hyperbolic  logarithms 29 

4.  Legal  horse-power  of  steam-boilers  by  evaporation        .  .     36 

5.  Economy  and  gain  of  power  by  heating  the  feed-water  .     39 

6.  Horse-power  by  fire-grate  and  heating-surface        .         .  .40 
'  7.  Correction  of  horse-j>ower  for  height  of  chimney  .         .  .41 

8.  Consumption  of  coal  per  square  foot  of  grate  for  different 

heights  of  chimney  .......     41 

9.  Properties  of  air  for  combustion 45 

10.  Incomplete  combustion  with  different  quantity  of  air  supplied     47 

11.  Properties  and  ingredients  of  different  kinds  of  fuel      .         .     50 

12.  Percentage  of  power  or  fuel  gained  by  heating  feed- water     .     54 

13.  Products  of  combustion,  specific  gravity  and  volume     .         .     56 

14.  Water-gauge  for  chimney  draft 62 

15.  Area  of  safety-valves  and  velocity  of  steam  passing  into  air      71 

16.  Percentage  of  heat  or  power  gained  by  covering  steam-pipes     82 
17  to  22.  Strength  of  steam-boilers,  U.  S.  rule   .         .         .       92-97 
23.  Proportions  of  single- riveted  lap-joints  for  steam-boilers         .  102 
24  and  25.  Double-riveted  lap-joints,  proportions  of    .         .         .104 

26.  Coefficient  for  strength  of  lap-joints  in  steam-boilers      .         .105 

27.  Distance  in  inches  between  boiler-stay  for  steam-boilers         .  109 

28.  Specific  heat  of  permanent  gases  .         .         .         .         .         .119 

29.  Horse- power  of  chimneys 123 

30.  Properties  of  permanent  gases 124-127 

31.  Compression  of  air  by  external  force 134 

32.  Expansion  of  air  by  external  force       .         .         .         .         .  135 

33.  Volume  of  carbonic  acid  gas 137 

34.  Pressure  and  temperature  of  carbonic  acid  vapor          .         .  138 

35.  Comparison  of  volume  and  temperature  of  steam          .         .144 
36  to  45.  Properties  of  water  and  steam     ....    150-159 
46  and  47.  Mean  pressure  of  steam 160 

48.  Properties  of  different  kinds  of  vapors          ....  167 

49.  Distillation  and  inflammation  of  petroleum  oils    .         .         .  169 


STANDARD  NOTATION   OF  LETTERS. 


IT  has  been  attempted  throughout  this  work  to  adopt  a  standard 
notation  of  letters,  for  which  some  new  characters  have  been  added 
to  distinguish  different  quantities  which  have  heretofore  been  denoted 
by  identical  letters. 

It  is  of  great  importance  in  technical  works  that  the  formula 
should  be  clear  at  a  glance  without  special  reference  to  the  meaning 
of  its  characters. 

The  characters  B,  a,  T,  t,  rf,  V,  IP,  %?,  £  and  c  have  been  made 
especially  for  this  work. 

The  letters  T  and  t  denote  time,  T  and  t  temperature.  F  and  v 
denote  velocity,  ^  and  3f  volume.  P  and  p  denote  pressure,  and  ^ 
power. 

Mr.  W.  Barnet  Le  Van  proposed  the  letter  "^  to  denote  volume  of 
steam,  as  a  distinction  from  F,  which  is  used  to  denote  velocity. 

Differential  is  denoted  by  8,  and  is  placed  close  to  its  variable 
quantity,  like  fix  (not  c  x),  because  the  two  letters  denote  only  a 
single  quantity. 

The  common  letter  d  is  needed  for  denoting  diameter,  distance, 
depth  and  other  quantities. 

The  character  8  is  more  distinct  in  denoting  the  differential,  which 
is  not  a  common  notation,  and  should  be  conspicuous  like  the  integral 

The  character  8  ought  not  to  be  used  for  any  other  notation  but 
differential. 

The  special  characters  B  and  a,  denoting  grate  surface  and  heat- 
ing surface,  are  new  and  explicit  for  steam-boiler  notations. 

The  characters  "$,  denoting  weight  in  pounds  per  cubic  foot,  and 
6  cubic  feet  per  pound,  are  also  explicit  notations  which  ought  to  be 
permanently  maintained. 
10 


NOTATION  OF  LETTERS. 


11 


P 
p 
*ft 
.0" 
H' 
L 
U 


W 

w  • 
Ibs. 


STEAM   NOTATION. 

absolute  steam-pressure,  Ibs. 

per  sq.  in. 
steam   pressure   above   that 

of  atmosphere. 
steam  volume  compared  with 

that  of  its  water. 
units  of  heat  per  pound  in 

steam. 
units  of  heat  per  cubic  foot 

in  steam. 
latent   heat   per    pound    in 

steam. 
latent  heat  per  cubic  foot  in 

steam. 

pounds  per  cubic  foot. 
cubic  feet  per  pound. 
temperature  Fahr.  of  steam. 
thermodynamic  equivalent. 
grade  of  expansion  of  steam. 

WATER   NOTATION. 

volume    of   water,   that    at 

39°  or  40°  =  1. 
temperature  Fahr.  of  water. 
latent   heat   per    pound    in 

water  from  32°. 
latent  heat  per   cubic   foot 

of  water. 
units  of  heat  per  pound  of 

water. 
units  of  heat  per  cubic  foot 

of  water. 
weight  in  pounds  per  cubic 

foot  of  water. 
fraction  of  a  cubic  foot  per 

pound  of  water. 
cubic  feet  of  water. 
cubic  inches  of  water. 
pounds  of  water. 


DYNAMICAL  NOTATIONS. 

F=  force  in  pounds  avoirdupois. 

F=  velocity  in  feet  per  second. 

T=  time  of  action  in  seconds. 

*S=  V  T,  space  in  feet  or  cubic 
feet. 

^  =  F  V,  power  in  effects  or 
second  foot-pounds. 

IP  =  550  £,  horse-power,  Watt's 
unit. 

K=F  V  T,  work  in  foot- 
pounds. 

STEAM-BOILER   NOTATION. 

H  =  area  of  firegrate  in  square 
feet. 

Q  =  area  of  heating  surface  in 
square  feet. 

D  =  diameter  of  boiler  in  inches. 

d  =  diameter  of  staybolts  in  in- 
ches. 

t  =  thickness  of  boiler-plates  in 
inches. 

S  =  breaking-strain  per  square 
inch  of  iron. 

H  =  height  of  chimney  in  feet. 

A  =  cross-area  of  chimney  in 
square  feet. 

PERMANENT  GASES  NOTATION. 

"ft  and  %f  =  volumes. 
T  and  t  =  actual  temperatures. 
C  and  t  =  ideal  temperatures. 
P  and  p  =  absolute  pressures. 

^  =  pound  per  cubic  foot. 
h  =  units  of  heat. 
S=*  specific  heat,  constant 

volume. 

s  =  specific  heat,  any  vol- 
ume and  pressure. 
W=  weight  of  gas  in  pounds. 


MECHANICS. 


DEFINITIONS  OF  THE  PRINCIPAL.  TERMS  IN 
MECHANICS. 

MECHANICS  is  that  branch  of  natural  philosophy  which  treats 
of  the  three  simple  physical  elements  force,  velocity  and  time, 
with  their  combinations,  constituting  the  functions  power,  space 
and  -work. 

Mechanics  is  divided  into  two  distinct  parts — namely,  Statics 
and  Dynamics. 

STATICS  is  the  science  of  forces  in  equilibrium  or  at  rest. 

DYNAMICS  is  the  science  of  forces  in  motion,  producing  power 
and  work. 

QUANTITY  is  any  principle  or  magnitude  which  can  be  in- 
creased or  diminished  by  augmentation  or  abatement  of  homogeneous 
parts,  and  which  can  be  expressed  by  a  number. 

ELEMENT  is  an  essential  principle  which  cannot  be  resolved  into 
two  or  more  different  principles. 

FUNCTION  is  any  compound  result  or  product  of  two  or  more 
different  elements. 

A  function  is  resolved  by  dividing  it  with  one  or  more  of  its 
elements. 

Force,  velocity  and  time  are  simple  physical  elements. 
Power,  space  and  work  are  functions  of  those  elements. 

These  six  terms  represent  the  principal  elements  and  functions  in 
Mechanics.  All  creation,  work  or  action,  of  whatever  kind,  whether 
mechanical,  chemical  or  derived  from  light,  heat,  electricity  or  mag- 
netism— all  that  has  been  and  is  to  be  done  or  undone — is  compre- 
hended by  the  product  of  force,  velocity  and  time. 


DEFINITIONS  OF  TEEMS.  13 

FORCE  is  any  action  which  can  be  expressed  simply  by  weight, 
without  regard  to  motion,  time,  power  or  work.  It  is  an  essential 
principle  which  cannot  be  resolved  into  two  or  more  different  prin- 
ciples, and  is  therefore  a  simple  element. 

VELOCITY  is  speed  or  rate  of  motion.  It  is  an  essential  prin- 
ciple which  cannot  be  resolved  into  two  or  more  principles,  and  is 
therefore  a  simple  element. 

TIME  is  duration  or  that  measured  by  a  clock.  It  is  an  essential 
principle  which  cannot  be  resolved  into  two  or  more  different  prin- 
ciples, and  is  therefore  a  simple  element. 

POWER  is  the  product  of  the  first  and  second  elements,  force  and 
velocity,  and  is  therefore  a  function. 

SPACE  is  the  product  of  the  second  and  third  elements,  velocity 
and  time,  and  is  therefore  a  function. 

WORK  is  the  product  of  the  three  simple  elements  force,  velo- 
city and  time,  and  is  therefore  a  function. 

Work  is  also  the  product  of  the  element  force  and  function  space, 
because  the  function  space  contains  the  elements  velocity  and  time. 

W^ork  is  also  the  product  of  the  function  power  and  element  time, 
because  the  function  power  contains  the  elements  force  and  velocity. 

MOMENTUMS  are  of  two  kinds — namely,  Static  and  Dy- 


STATIC-MOMENTUM  is  the  product  of  force  and  the  lever 
upon  which  it  acts,  and  is  therefore  a  function. 

DYNAMIC-MOMENTUM  is  the  product  of  mass  and  its 
velocity,  which  is  equal  to  the  product  of  the  force  and  time  that 
has  produced  the  velocity  of  the  mass,  and  is  therefore  a  function. 

MASS  is  the  real  quantity  of  matter  in  a  body,  and  is  propor- 
tionate to  weight  when  compared  in  one  and  the  same  locality. 
Mass  is  an  essential  principle  which  cannot  be  resolved  into  two  or 
more  principles,  and  is  therefore  a  simple  element. 

The  new  treatise  on  "Elements  of  Mechanics,"  published  by 
Porter  &  Coates,  Philadelphia,  gives  complete  explanations,  with 
practical  examples  of  the  mechanical  elements  and  functions. 


14 


MECHANICS. 


STATICS. 

ALGEBRAICAL  AND  GEOMETRICAL  EXPRESSIONS  OF  THE 
FUNDAMENTAL  PRINCIPLES  OF  STATICS. 

Levers  of  Different  Kinds. 


First. 

~  | 

Third. 

fz  T  ^ 

!<  «  a   i* 

fg  ' 

/yv\ 

F:  W  =  l:L. 

.P:  TF=/:i. 

F:  FF=/:i. 

Static  Momentum. 
^£=1*7. 

Static  Momentum. 

Fi=TF;. 

Static  Momentum. 

FL=  Wl. 

-f- 

F"T' 

*-f 

"    I    ' 

r"T' 

"~T~' 

.Pa 

Fa 

i     Fa 

~TF+X 

FF-F* 

'    F-W' 

TFa 

TFa 

L       Wa 

W+F' 

JF-1?' 

F-W' 

DYNAMICS. 

ALGEBRAICAL  AND  GEOMETRICAL  EXPRESSIONS  OF  THE 
FUNDAMENTAL  PRINCIPLES  OF  DYNAMICS. 


Elements. 
Force  =  F. 
Velocity  -F. 
Time  =  T. 


Functions. 
Power  £  =  F  V. 
Space  8-  V  T. 
WorkK-FVT. 
=     M  y\ 


These  are  the  fundamental  principles  in  Mechanics. 


REJECTED   TERMS.  15 


REJECTED  TERMS   IN  MECHANICS. 

The  author  has  rejected  a  great  number  of  terms  in  Mechanics 
which  are  considered  useless,  confusing  and  without  definite  mean- 
ings, a  list  of  which  is  given  below  and  on  the  next  page. 

High-sounding  terms  without  definite  meaning  render  the  subject 
of  Mechanics  difficult  to  learn,  for  which  reason  the  author  has  de- 
cided to  employ  only  such  terms  as  are  used  in  the  shop. 

The  language  of  Mechanics  used  in  schools  and  text-books  differs  so 
much  from  that  used  in  practice  that  when  a  graduate  student  con- 
verses with  a  practical  man  on  that  subject,  they  do  not  understand 
each  other,  and  the  latter  derides  the  former  as  theoretical.  This  is 
the  principal  reason  why  theoretical  sciences  are  so  little  available  in 
practice. 

In  the  Appendix  to  this  book  is  given  an  example  of  the  language 
of  Mechanics  as  used  in  institutions  of  learning,  from  which  it  will  be 
perceived  that  the  author  has  good  reasons  for  having  undertaken  a 
revision  of  the  subject. 

The  list  of  rejected  terms  on  the  next  page  is  taken  from  the  new 
treatise  of  "Elements  of  Mechanics,"  to  which  the  following  list  of 
expressions  and  terms  is  added  : 

Mechanics  of  a  material  point       .         .         .  W.  p.  165. 

Forces  in  space W.  p.  182. 

Principles  of  virtual  velocity        .         .         .  W.  p.  185. 

Couples W.  p.  200. 

Dynamical  stability      .         .        .        .         .  W.  p.  269. 

Modulus  of  a  machine  M. 

Intensity  of  force W.  p.  164. 

Strength  of  impact       .  .         .         .  W.  p.  102. 

Intensity  of  the  effort B.  p.  49. 

Effort  of  mechanical  work    .         .         .         .  B.  p.  57. 

Living  force  impressed          .         .         .         .  B.  p.  82. 

Equilibrium  in  a  knot          .        .        .         .  W.  p.  281. 

These  kinds  of  terms  and  expressions  convey  no  definite  meaning, 
and  are  not  used  in  practice. 


REJECTED   TERMS. 


DYNAMICAL    TERMS. 


Rejected  Terms. 

Effort  of  force. 

Efficiency  of  force. 

Acting  force. 

Force  of  motion. 

Working  force. 

Quantity  of  moving  force. 

Quantity  of  motion. 

Mode  of  motion. 

Mode  of  force. 

Moment  of  activity. 

Mechanical  power. 

Mechanical  effect. 

Quantity  of  action. 

Efficiency. 

Rate  of  work. 

Dynamic  effect. 

Quantity  of  work. 

Actual  total  quantity  of  work. 

Total  amount  of  work. 

Actuated  work. 

Vis- viva. 

Living  force. 

Energy. 

Actual  energy. 

Potential  energy. 

Kinetic  energy. 

Energy  of  motion. 

Energy  of  force. 

Heat  a  form  of  energy. 

Heat  a  mode  of  motion. 

Mechanical  potential  energy. 

Quantity  of  energy. 

Stored  energy. 

Intrinsic  energy. 

Total  actual  energy. 

Work  of  energy. 

Equation  of  energy. 

Equality  of  energy. 


Reason  for  Rejection. 

Means  simply  force. 

All  forces  act. 
Means  motive  force. 


Has  no  definite  meaning. 


Means  simply  power. 


Used  for  power  or  work. 
Means  simply  work. 


Formula  for  work. 
Primitive  and  realized  work. 


141 

STEAM  ENGINEERING. 


§  1 .  A  STEAM-ENGINE  is  only  a  tool  by  which  the  power  generated 
in  the  steam-boiler  is  transmitted  to  where  the  work  is  executed,  like 
a  water-wheel  which  transmits  the  power  of  a  waterfall  to  its  des- 
tination. 

,In  hydraulics  we  define  correctly  the  power  of  a  waterfall,  which 
is  called  "the  natural  effect  of  the  fall,"  in  distinction  from  the  power 
transmitted  by  the  water-wheel ;  but  in  steam  engineering  we  have 
heretofore  not  defined  correctly  the  natural  effect  generated  in  the 
steam-boiler  as  distinct  from  that  transmitted  by  the  engine. 

A  badly-constructed  water-wheel  may  transmit  only  twenty  per 
cent,  of  the  natural  effect  of  the  waterfall,  whilst  a  properly-con- 
structed wheel  may  transmit  as  high  as  eighty  per  cent,  or  more  of 
the  power  of  the  fall.  Such  is  the  case  also  with  steam-engines. 
A  badly-constructed  steam-engine  transmits  a  much  smaller  percent- 
age of  the  natural  effect  from  the  boiler  than  does  a  better  constructed 
engine.  Therefore  the  power  obtained  by  indicator  diagrams  from 
the  engine  is  not  a  correct  measure  of  the  power  or  steaming  capacity 
of  the  boiler. 

§  2.  From  experimental  data  we  have  given  the  volume  of  steam 
generated  by  the  evaporation  of  a  given  volume  of  water,  which 
steam  volume  multiplied  by  the  steam  pressure,  gives  the  work  done 
by  the  steam.  This  work  divided  by  the  time  in  which  it  is  exe- 
cuted, gives  the  natural  effect  or  power  of  the  evaporation,  independ- 
ent of  the  power  transmitted  by  the  steam-engine,  supposing  that  the 
steam  is  fully  admitted  throughout  the  stroke  of  the  piston. 

When  the  steam  is  expanded  in  the  steam-cylinder,  the  above  de- 
fined power  multiplied  by  1  +  the  hyperbolic  logarithm  for  the  expan- 
sion, gives  the  natural  effect  of  the  steam. 

§  3.  The  primary  source  of  power  is  derived  from  the  combustion 
of  fuel  in  the  furnace  generating  heat  which  penetrates  the  heating 
surface  into  the  water  which  is  thus  evaporated. 

The  act  of  combustion  is  power,  which,  multiplied  by  time,  is  work. 

The  act  of  evaporation  is  power,  which,  multiplied  by  time,  is  work. 


18 


STEAM  ENGINEERING. 


Fig.  1. 


The  natural  effect  or  power  of  combustion  is  not  wholly  transmitted 
to  evaporation,  but  part  of  it  escapes  through  the  chimney. 

The  physical  constitution  of  heat  is  not  yet  well  understood,  for 
which  reason  we  cannot  give  an  intelligent  explanation  of  the  dy- 
namic elements  of  combustion  and  evaporation ;  but  one  thing  ap- 
pears to  be  certain — namely,  that  the  temperature  of  the  heat  repre- 
sents force,  which  is  the  origin  of  all  power  and  work.  It  is  also 
known  and  demonstrated  that  heat  is  convertible  into  work ;  and  con- 
sequently, heat  must  be  the  product  of  the  three  simple  physical  ele- 
ments, force,  velocity  and  time. 

If  the  temperature  of  the  heat  represents  force,  then  the  space  occu- 
pied by  the  heat  must  evidently  represent  the  product  of  velocity  and 
time. 

Here  it  is  necessary  to  refer  the  reader  to  the  author's  New  Treatise 
on  Elements  of  Mechanics,  published  by  Porter  &  Coates, 
Philadelphia. 

a  §  4.  The  expression  "horse-power  of  a  steam-boiler" 
is  understood  to  mean  the  horse-power  of  evaporation  in 
the  boiler,  which  power  is  derived  from  the  heat  in  the 
furnace. 

For  simplicity  of  illustration,  let  the  steam-boiler  be 
represented  by  the  tube  A  B,  of  one  square  foot  sec- 
tion, with  a  bottom  at  A  and  open  at  the  top  B. 

One  cubic  foot  of  water  W  is  placed  on  the  bottom 
in  the  tube  and  covered  with  a  tight  piston  loaded  with 
a  weight  Q. 

A  burning  lamp  L  is  placed  under  the  bottom  to 
heat  the  water  for  making  steam. 

The  steam-pressure  thus  generated  will  raise  the  pis- 
ton with  the  weight  Q  to  a  height  S,  and  the  work 
accomplished  by  the  steam  will  be  the  weight  Q  (which 
must  include  the  pressure  of  the  atmosphere  on  one 
square  foot,  and  also  the  weight  of  the  piston,  which  is 
supposed  to  move  without  friction)  multiplied  by  the 
height  S  which  the  piston  is  raised.  This  work  divided 
by  the  time  in  which  it  is  accomplished,  gives  the  power 
of  evaporation,  which  is  generally  termed  the  power  of 
the  boiler. 

Assume  the  steam-pressure  to  be  100  pounds  to  the 
square  inch  above  vacuum,  then  100  x  144  =  14400 
pounds,  the  required  weight  of  Q.  When  all  the  water 
— that  is,  one  cubic  foot — is  evaporated,  the  steam 


Q. 


NATURAL  EFFECT  OF  STEAM.  19 

volume  will  be  267.8  cubic  feet ;  and  as  the  section  of  the  tube  is 
one  square  foot,  the  piston  must  have  been  lifted  267.8  feet,  minus 
the  one  foot  occupied  by  the  water,  or  S=  266.8  feet. 

The  work  accomplished  by  the  steam  will  then  be  266.8x14400 
=  3,831,920  foot-pounds. 

Suppose  this  work  to  be  accomplished  in  the  time  of  one  minute, 
and  the  power  of  the  evaporation  will  be, 

3831920     . 

—  =  116.12  horse-power. 
33000 

This  should  be  the  natural  effect  of  the  steam  without  expansion. 

§  5.  Now,  diminish  the  weight  Q  gradually,  so  as  to  allow  the  steam 
to  expand — say  to  double  its  volume.  Then,  the  hyperbolic  logarithm 
for  2  =  0.69315,  multiplied  by  the  primitive  horse-power  116.12,  gives 
80.488  horse-power  gained- by  the  expansion  alone,  and  the  gross  effect 
of  the  steam  will  be  116.12  +  80.488  =  196.608  horse-power. 

It  will  be  noticed  that  the  one  cubic  foot  of  steam  which  displaced 
the  water  was  lost  in  the  natural  effect  of  the  evaporation  ;  and  that 
is  the  steam-volume  required  for  pumping  the  feed-water  into  the 
boiler  in  order  to  maintain  a  constant  height  of  water-level. 

By  the  aid  of  algebra  the  above  argument  can  be  made  general  for 
any  steam-pressure  and  dimension  of  boiler,  for  which  we  will  adopt 
the  following  notation  of  letters : 

W=  cubic  feet  of  water  of  temperature  32°  Fahr.  evaporated  in  the 
time  T  seconds. 

P=  steam-pressure  in  pounds  per  square  inch  above  vacuum. 

^r  =  volume  of  steam  compared  with  that  of  its  water  at  32°  Fahr. 
This  volume  can  be  found  in  Nystrom's  Pocket-Book,  pages 
398,  399,  calculated  from  the  formula  of  Fairbairn  and 
Tate,  which  is  yet  the  highest  authority  on  that  subject. 

£  =  power  in  effects,  or  second-foot-pounds. 

EP  =  horse-power  of  evaporation. 
S  =  space  generated  by  the  steam  in  cubic  feet. 

jP=  force  in  pounds. 

V=  velocity  in  feet  per  second. 
T=  time  of  operation  in  seconds. 

K-=  work  in  foot-pounds  done  in  the  time  T  by  the  steam. 

X=  grade  of  expansion  of  the  steam. 

The  Fairbairn's  formula  for  the  volume  of  steam  compared  with 
water  at  32°  Fahr.  is 


20  STEAM  ENGINEERING. 

See  arguments  on  dryness  and  humidity  of  steam,  in  regard  to  Fair- 
bairn's  steam-volume. 

The  space  S,  generated  by  the  steam  in  cubic  feet,  will  be 

S=W(tf-l')      ....         1 

§  6.  This  space  multiplied  by  the  steam-pressure  will  be  the  work 
done  by  the  steam;  and  as  the  space  or  steam-volume  is  expressed 
in  cubic  feet,  the  steam-pressure  must  be  expressed  per  square  foot, 
or  144  P. 

The  unit  1  in  the  factor  (^-1)  represents  the  primitive  volume 
occupied  by  the  water  evaporated,  and  which  unit  of  volume  is  con- 
sumed in  feeding  the  boiler  with  water,  as  before  explained. 

The  work  accomplished  by  the  steam  will  then  be  in  foot-pounds. 
K=  TF(^-l)  144  P       ...        2 

Work  is  the  product  of  the  three  simple  physical  elements,  force 
F,  velocity  V  and  time  T,  or 

K=FVT        ....         3 

Power  £  is  the  product  of  the  two  elements  force  F  and  velocity 
F,  or 

%=FV          ....        4 

This  power  is  expressed  in  effects,  each  of  a  force  of  one  pound, 
moving  with  a  velocity  of  one  foot  per  second,  of  which  there  are  550 
effects  per  horse-power,  or 

FV 

H>  =  —        .....         5 
550 

The  formulas  2  and  3  give  the  work 

=      T          .        .        6 


Work  is  the  product  of  power  and  time,  and  consequently,  if  we 
eliminate  the  time  from  the  work,  we  obtain  the  power,  or 


of  which  the  horse-power  will  be 


This  formula  reduces  itself  to 

H>^P(t-l)  9 

3.819  T 

This  is  the  natural  effect  or  gross  horse-power  of  evaporation  of 
water  into  steam  without  expansion. 


NATURAL   EFFECT  OF  STEAM.  21 

§  7.  The  quantity  of  water  which  must'  be  evaporated  under  a 
pressure  P  in  the  time  T  in  order  to  generate  a  given  horse-power 
will  be 


Assuming  the  quantity  of  water  evaporated  per  hour  as  a  measure 
of  gross  horse-power  of  evaporation,  we  have  the  time  27=3600  sec- 
onds. Then  3.819  x  3600  =  13748.4.  Insert  this  value  for  3.819  T  in 
formula  9,  and  the  gross  horse-power  of  evaporation  per  hour  will  be 

WP(#    1) 
13748.4        '        •        •        • 

The  quantity  of  water  evaporated  per  hour  per  gross  horse-power 
will  be 

;„    13748.4IP  19 

Logarithm  for  13748.4  =  4.1382522. 

§  8.  The  steam  volume  tf  is  compared  with  that  of  water  at  32° 
Fahr. ;  therefore,  in  determining  the  gross  horse-power  of  evaporation 
of  water  of  a  higher  temperature,  the  action  must  be  reduced  to  that 
from  water  at  32°.  This  reduction  is  accomplished  by  the  following 
formula,  in  which  letters  denote : 

t  =  actual  temperature  of  the  feed-water  supposed  to  be  higher 
than  32°. 

T  =  temperature  of  the  steam  of  pressure  P. 

W=  cubic  feet  of  water  that  would  have  been  evaporated  from  the 
temperature  32°. 

W  =  cubic  feet  of  feed-water  evaporated  from  temperature  t. 

$"=  volume  of  water  at  temperature  t,  compared  with  that  at  39°. 

w=  W'f  1082  +  0.305  1  13 


This  formula  is  derived  from  the  units  of  heat  required  to  evap- 
orate water  of  temperature  32°  to  steam  of  temperature  T. 

This  reduction  is  required  for  comparing  the  relative  steaming 
capacity  of  different  boilers  fed  with  water  of  different  temperatures. 
The  reduction  varies  very  little  for  different  pressures — namely,  from 
20  to  150  pounds  the  difference  will  show  only  on  the  third  decimal ; 
for  which  reason  we  may  practically  omit  the  steam-pressure  and 
calculate  the  reduction  only  for  different  temperatures  of  the  feed- 
water,  as  is  done  in  the  following  Table  I. 


22 


STEAM  ENGINEERING. 


When  the  exact  relation  between  pressure,  temperature  and  volume 
of  steam  is  known,  the  reduction  will  likely  be  independent  of  the 
pressure  or  temperature  of  the  steam.  See  Humidity  of  Steam. 

TABLE  I. 
Reduction  for  Temperature  of  Feed- water. 


Temp.  /. 

Reduction  Jl. 

Logarithm. 

Temp.  t. 

Reduction  R. 

Logarithm. 

40 

0.9932 

9.9970367 

130 

0.9105 

9.9592620 

50 

0.9851 

9.9934803 

140 

0.9000 

9.9546693 

60 

0.9761 

9.9895039 

150 

0.8912 

9.9499637 

70 

0.9671 

9.9854546 

160 

0.8815 

9.9451979 

80 

0.9577 

9.9812455 

170 

0.8719 

9.9404765 

90 

0.9486 

9.9770612 

180 

0.8625 

9.9357359 

100 

0.9392 

9.9727643 

190 

0.8529 

9.9308916 

110 

0.9296 

9.9683116 

200 

0.8432 

9.9259440 

120 

0.9199 

9.9637468 

212 

0.8317 

9.9199515 

§  9.  The  actual  quantity  of  feed-water  of  temperature  t,  multiplied 
by  the  reduction  in  the  table,  gives  the  quantity  of  water  that  would 
have  been  evaporated  when  heated  from  temperature  32°  Fahr. 

Example  11.  A  steam-boiler  evaporating  W=  125  cubic  feet  of  water 
per  hour  under  a  pressure  of  P=  75  pounds  to  the  square  inch  above 
vacuum,  or  60  pounds  above  the  atmosphere,  the  temperature  of  the 
feed- water  being  t  =  110°.  Required  the  natural  effect  or  horse-power 
of  the  evaporation  ? 

Formula  11.         ff  =  125*75  <348-15'  ^236.73  horses. 
13748.4 

That  is,  0.528  cubic  feet  of  water  evaporated  per  hour  per  horse- 
power, or  1.893  horse-power  per  cubic  foot  of  water  evaporated  per 
hour. 

Making  correction  for  the  temperature  of  the  feed-water  110°  (see 
Table),  the  horse-power  will  be  168.53x0.9392  =  220.06  horse-power, 
the  natural  effect  of  the  evaporation. 

Example  12.  What  quantity  of  water  of  temperature  t  =  90°  must 
be  evaporated  under  a  pressure  of  P=90  pounds  to  the  square  inch 
in  order  to  generate  a  natural  effect  of  IP  =  150  horse-power  ? 
13748.4x150 


Formula  12. 


=  78.043  cubic  feet. 


90(294.61-1) 

This  volume  corrected   for  temperature   gives   78.043  :  0.9486  = 
82.275  cubic  feet,  the  quantity  of  water  required. 


NATURAL  EFFECT  OF  STEAM. 


23 


TABLE  II. 

Natural  effect  of  evaporation  of  water  by  heat  converted 
into  horsepower. 


Steam 
pressure 
ab.  vacm. 

Water  eva 
1 

Cubic  feet. 

3orated  per 
orsepower. 

Cubic  in. 

hour  per 
Pounds. 

Horse- 
power 
per  cub.  ft. 

Equiva- 
lent work 
per  unit 
of  heat. 

P 

w 

W 

Ibs. 

H> 

J 

5 

0.6024 

1041.0 

29.852 

1.6600 

46.584 

10 

0.5796 

1002.0 

28.723 

1.7253 

48.032 

14.7 

0.5701 

985.2 

28.252 

1.7540 

48.583 

20 

0.5641 

974.7 

27.954 

1.7727 

48.902 

25 

0.5593 

966.5 

27.717 

1.7879 

49.040 

30 

0.5553 

959.6 

27.518 

1.8008 

49.403 

35 

0.5516 

'  953.2 

27.337 

1.8130 

49.665 

40 

0.5483 

947.4 

27.170 

1.8238 

49.832 

45 

0.5451 

941.9 

27.012 

1.8345 

50.150 

50 

0.5420 

936.6 

26.861 

1.8450 

50.244 

55 

0.5391 

931.5 

26.715 

1.8549 

50.440 

60 

0.5362 

926.6 

26.573 

1.8649 

50.651 

65 

0.5334 

921.6 

26.429 

1.8747 

50.861 

70 

0.5305 

917.1 

26.300 

1.8850 

51.060 

75 

0.5280 

912.5 

26.168 

1.8936 

51.265 

80 

0.5254 

907.9 

26.038 

1.9033 

51.470 

85 

0.5228 

903.5 

25.910 

1.9127 

51.670 

90 

0.5203 

899.1 

25.783 

1.9219 

51.865 

95 

0.5178 

894.7 

25.660 

1.9312 

52.077 

100 

0.5153 

890.5 

25.537 

1.9406 

52.264 

105 

0.5129 

886.2 

25.415 

1.9497 

52.513 

110 

0.5104 

882.0 

25.295 

1.9592 

52.722 

115 

0.5081 

877.9   25.177 

1.9681 

53.053 

120 

0.5057 

873.8   25.060 

1.9774 

53.137 

125 

0.5034 

869.8   24.945 

1.9865 

53.351 

130 
135 

0.5008 
0.4988 

865.3 
861.9 

i  24.815 
24.718 

1.9968 

2.0048 

53.572 
53.788 

140 

0.4965 

858.0 

24.606 

2.0140 

54.000 

145 

0.4943 

854.1 

24.494 

2.0230 

54.206 

150 

0.4921 

850:4 

24.387 

2.0321 

54.427 

24 


STEAM  ENGINEERING. 


The  preceding  Table  II.  gives  the  horse-power  per  evaporation  per 
hour  of  water,  expressed  either  in  cubic  feet,  cubic  inches  or  pounds  ; 
also  the  thermo-dynamic  equivalent  of  heat  as  realized  by  the  steam 
without  expansion. 

When  the  water  evaporated  is  expressed  in  pounds,  the  formulas 
11  and  12  will  appear  as  follows  : 

Ibs  =  pounds  of  water  evaporated  in  the  boiler  per  hour. 


15 


The  correction  for  temperature  of  feed-water  will  be  the  same  by 
Table  I.  as  when  the  water  is  expressed  in  cubic  feet.  One  cubic  foot 
of  water  at  32  weighs  62.387  pounds. 

Fig.  2. 


857721 

Logarithm  for  857721  =  5.9333463. 
857721  IP 


EXPANSION    OF   STEAM. 

§  10.  When  steam  is  working  expansively,  more  power  is  realized 
per  water  evaporated  than  that  given  by  the  Formula  11. 

Let  A  B  C  D,  fig.  2,  represent  a  section  of  a  steam  cylinder  of  in- 
definite length,  in  which  is  fitted  a  piston  a  b,  upon  which  the  full 
steam-pressure  P  is  acting  in  the  distance  /,  enclosing  the  steam-vol- 
ume A  B  a  b,  to  be  expanded.  The  work  accomplished  by  the  full 
steam- pressure  P  can  be  represented  by  the  area  A  B  a  b,  or  P  I. 
When  the  admittance  of  steam  is  cut  off,  the  piston  is  moved  by  the 
expansion  of  the  steam,  and  the  pressure  decreases  as  the  steam-vol- 
ume increases ;  so  that  when  the  volume  is  doubled  the  pressure  will 
be  one-half  or  0.5  P,  and  when  the  piston  has  moved  two  volumes  by 
the  expansion — that  is,  three  volumes  in  all — the  pressure  will  be 
JPata'6'. 

Let  the  line  A  B  represent  the  axis  of  ordinates  and  B  C  the  axis 
of  abscissa. 


EXPANSION  OF  STEAM.  25 

x  =  distance  generated  by  expansion. 

y  =  ordinate  pressure  of  the  expanded  steam. 

Then  P:y  =*+*:*          ...         1 


§  11.  Calculate  the  ordinate  pressure  y  for  several  positions  of  the 
piston,  and  set  them  off  as  shown  in  the  figure.  Join  these  ordinates 
by  the  curve  acde,  and  the  work  done  by  the  expansion  is  represented 
by  the  area  bounded  within  that  curve  and  P  x  y. 

k  =  area,  or  work  of  expansion  alone,  expressed  in  units  of  P  I,  the 
work  done  by  the  full  steam-pressure. 

Then  -    dk  = 


l+x 

We  have  assumed  P  I  as  unit  for  the  measurement,  in  which  case 
P=  1  and  1  =  1,  and  the  differential  work  will  be 


1+x 


k  =   I =  hyp.log.  ( 1  +  x) 


The  factor  (l+x)  represents  the  whole  motion  of  the  piston,  of 
which  x  is  the  portion  worked  with  expansion. 
8  =  whole  stroke  of  the  piston. 
I  =  part  of  the  stroke  worked  with  full  steam. 
X=  grade  of  expansion — that  is,  when  the  steam  is  expanded  to 

double  its  volume,  then  X=  2 ;  when  three  times  the  volume, 

X=  3,  and  so  on. 

jr=p(i+*)      ....      6 

The  work  done  by  the  expansion  will  then  be 

k  =  hyp. log. X=  hyp. log.-    ...         7 

That  is  to  say,  the  effect  gained  by  the  expansion  is  equal  to  the  hy- 
perbolic logarithm  for  the  expansion. 

When  the  steam  is  expanded  say  four  times,  then  hyp.  log. 
4  =  1.38629,  or  the  gain  will  be  138  per  cent,  over  the  effect  of  that 
worked  with  full  steam,  and  the  gross  effect  K  will  be  238  per  cent. 

jfiT=  1  -+  hyp.log.X=  1  +  hyp.log.-         .         .         8 


STEAM   ENGINEERING. 


The  natural  effect  or  horse-power  of  evaporation  without  expan- 


o 
13748.4 

which  multiplied  by  (  1  +  hyp.  log.  X^),  will  be  the  natural  effect  or 
horse-power  of  evaporation  with  expansion,  or 


.. 
1348.4 

§  12.  This  formula  gives  the  natural  effect  of  evaporation  of  water 
into  steam,  and  which,  divided  into  the  power  given  out  or  transmit- 
ted by  a  steam-engine,  gives  the  efficiency  of  that  steam-engine,  as 
the  natural  effect  of  a  waterfall  divided  into  the  power  transmitted  by 
the  wheel  gives  the  efficiency  of  that  water-wheel.  A  compound  en- 
gine working  with  a  high  degree  of  expansion  and  condensation  of 
the  steam  may  utilize  or  transmit  as  high  as  80  per  cent,  of  the  nat- 
ural effect  of  the  steam,  whilst  a  high-pressure  or  non-condensing  en- 
gine working  against  atmospheric  pressure  may  transmit  only  40  per 
cent,  of  the  natural  effect. 

The  expansion  X  in  compound  engines  is  equal  to  the  volume  of 
full  steam  in  the  small  cylinder,  divided  into  the  cubic  content  of 
both  cylinders. 

The  cubic  content  of  one  steam-port  in  the  small  cylinder  should 
be  included  in  the  volume  of  full  steam,  and  the  cubic  content  of  one 
steam-port  of  each  cylinder  should  be  included  in  the  volume  of  the 
two  cylinders. 

Example  10.  A  set  of  steam-boilers,  evaporating  W=  640  cubic  feet 
of  water  per  hour,  under  a  pressure  of  P=65  pounds  to  the  square 
inch,  supply  steam  to  a  compound  engine  in  which  the  steam  is  ex- 
panded X=  8  times.  Required  the  natural  effect  of  the  steam  ? 

Hyp.log.8  =  2.07944.     ^  =  397.51. 

.     640x65x396.51x3.07944     , 
IP  =  —       -  -  --          -  =  3694.6   horse-power,   the  natural 

effect  required. 

It  is  supposed  in  this  example  that  the  temperature  of  the  feed- 
water  was  32°,  for  which  there  is  no  reduction.  The  water  evaporated 
per  hour  per  horse-power,  in  this  example,  is  0.1723  cubic  feet,  or 
5.773  horse-power  per  cubic  feet  evaporated  per  hour. 


POWER   OF  ATMOSPHERIC  PRESSURE.  27 

EFFECT   OF    ATMOSPHERIC    PRESSURE    OPPOSING    THE    NATURAL 
EFFECT    OF   THE    STEAM. 

§  13.  The  volume  of  air  displaced  by  the  steam  will  be 


This  volume,  multiplied  by  the  atmospheric  pressure  per  square 
foot,  will  be  the  work  of  resistance  of  the  atmosphere,  or 

F(^-l)Xx  14.7x144     ...        2 

That  is,  2116.8  TFX(^-l)  per  hour. 

This  work,  divided  by  550  x  3600  seconds,  gives  the  horse-power  of 
its  execution,  or  . 

2116.6  WXty-l)_  WXtf-V  3 

550x3600  935.37 

This  horse-power,  subtracted  from  Formula  10,  will  give  the  natural 
effect  of.  the  steam  above  that  of  the  atmosphere,  or 

g      WPtf-1)  (1  +  hyp.log.X)      WXtf-V) 
13748.4  935.37 


_ 

935.37     \          14.698 

This  should  be  the  natural  effect  of  steam  working  through  a  non- 
condensing  engine,  which,  divided  into  the  indicated  horse-power, 
gives  the  efficiency  of  the  motor. 

Example  5.  A  steam-boiler  evaporating  W=  85  cubic  feet  of  water 
per  hour,  under  a  pressure  of  P=100  pounds  to  the  square  inch,  sup- 
plies steam  to  a  non-condensing  engine,  cutting  off  at  one-third  the 
stroke,  making  X=3  the  expansion,  the  temperature  of  the  feed-water 
being  t  =  120°  Fahr.  Required  the  natural  effect  of  the  steam  above 
that  of  the  atmosphere  ? 

Hyp.log.Z  =  1.0986.     tf  =  267.8. 

85x266.8/100x2.0986      \ 
=  "  14.698      ~ 


Correction  for  temperature  of  feed-water  t  =  120°.  273.37  x  0.91  99 
=  251.48  horse-power  —  that  is,  0.338  cubic  feet  of  water  evaporated 
per  hour  per  horse-power,  or  2.958  horse-power  per  cubic  foot  of  water 
evaporated  per  hour. 


28  STEAM  ENGINEERING. 


MEAN    PRESSURE. 

§  14.  When  the  steam  is  expanded  in  the  cylinder,  the  mean 
pressure  throughout  the  stroke  of  piston  will  be  less  than  the  initial 
pressure. 

.F=mean  pressure  in  pounds  per  square  inch. 
P=  initial  pressure. 
X=  grade  of  expansion. 

s  =  length  of  stroke  in  inches. 

I  =  part  of  stroke  with  full  steam,  in  inches. 

PI 

The  mean  pressure   during  the  expansion  will   be  —   hyp.log.X, 


PI 
which,  added  to  —  ,  gives  the  mean  pressure  throughout  the  stroke,  or 

,    PI   PI, 
F=  —  •+  —  hyp.log.X         ...         1 

8         S 

X=*-,  which,  inserted  for  JTin  formula  1,  gives 

,    PI    PI  ,  s     PlL  ,     s\ 

jP=  —  +  —  hyp.log.  -  =  —  (  1  +  hyp.log.-]          .         2 

The  mean  pressure  for  different  pressures  and  expansion  of  steam  is 
calculated  by  this  formula,  and  given  in  a  table  farther  on. 


HYPERBOLIC   LOGARITHMS. 

§  15.  The  common  logarithm  multiplied  by  2.30258509  gives  the 
hyperbolic  logarithm,  and  the  hyperbolic  logarithm  multiplied  by 
0.43429448  gives  the  common  logarithm. 

The  following  table  contains  the  hyperbolic  logarithms  for  numbers 
up  to  39,  which  is  considered  sufficient  for  application  to  expansion 
of  steam. 


HYPERBOLIC  LOGARITHMS. 


29 


TABLE  III. 
Hyperbolic  Logarithms. 

No. 

Logarithms. 

No. 

Logarithms. 

No. 

Logarithms. 

No. 

Logarithms. 

1. 

0.00000 

4. 

1.38629 

7. 

1.94591 

10 

2.30258 

1.1 

0.09530 

4.1 

1.41096 

7.1 

1.96006 

11 

2.39589 

1.2 

0.18213 

4.2 

1.43505 

7.2 

1.97406 

12 

2.48491 

1.3 

0.26234 

4.3 

1.45859 

7.3 

1.98787 

13 

2.56494 

1.4 

0.33646 

4.4 

1.48161 

7.4 

2.00149 

14 

2.63906 

1.5 

0.40505 

4.5 

1.50408 

7.5 

2.01490 

15 

2.70805 

,  1.6 

0.46998 

4.6 

1.52603 

7.6 

2.02816 

16 

2.77259 

1.7 

0.53063 

4.7 

1.54753 

7.7 

2.04115 

17 

2.83321 

1.8 

0.58776 

4.8 

1.56859 

7.8 

2.05415 

18 

2.89037 

1.9 

0.64181 

4.9 

1.58922 

7.9 

2.06690 

19 

2.94444 

2. 

0.69315 

5. 

1.60944 

8. 

2.07944 

20 

2.99573 

2.1 

0.74190 

5.1 

1.62922 

8.1 

2.09190 

21 

3.04452 

2.2 

0.78843 

5.2 

1.64865 

8.2 

2.10418 

22 

3.09104 

2.3 

0.83287 

5.3 

1.66770 

8.3 

2.11632 

23 

3.13549 

2.4 

0.87544 

5.4 

1.68633 

8.4 

2.12830 

24 

3.17805 

2.5 

0.91629 

5.5 

1.70475 

8.5 

2.14007 

25 

3.21888 

2.6 

0.95548 

5.6 

1.72276 

8.6 

2.15082 

26 

3.25810 

2.7 

0.99323 

5.7 

1.74046 

8.7 

2.16338 

27 

3.29584 

2.8 

1.02962 

5.8 

1.75785 

8.8 

2.17482 

28 

3.33220 

2.9 

1.06473 

5.9 

1.77495 

8.9 

2.18615 

29 

3.36730 

3. 

1.09861 

6. 

1.79175 

9. 

2.19722 

30 

3.40120 

3.1 

1.13140 

6.1 

1.80827 

9.1 

2.20837 

31 

3.43399 

3.2 

1.16314 

6.2 

1.82545 

9.2 

2.21932 

32 

3.46574 

3.3 

1.19594 

6.3 

1.84055 

9.3 

2.23014 

33 

3.49651 

3.4 

1.22373 

6.4 

1.85629 

9.4 

2.24085 

34 

3.52636 

3.5 

1.25276 

6.5 

1.87180 

9.5 

2.25129 

35 

3.55535 

3.6 

1.28090 

6.6 

1-.88658 

9.6 

2.26191 

36 

3.58352 

3.7 

1.30834 

6.7 

1.90218 

9.7 

2.27228 

37 

3.61092 

3.8 

1.33046 

6.8 

1.91689 

9.8 

2.28255 

38 

3.63759 

3.9 

1.36099 

6.9 

1.93149 

9.9 

2.29171 

39 

3.66356 

30 


STEAM  ENGINEERING. 


THERMO-DYNAMICS. 

§  16.  The  thermo-dynamic  equivalent  of  heat  as  adopted  by  Joule 
is  772  foot-pounds  of  work  per  unit  of  heat. 

Different  authors  have  given  different  values  of  this  equivalent — 
namely, 


Foot-pounds. 

Joule 772 

Favre-  750 

Him 723 

Quintus 712 


Foot-pounds. 

Joule       in  1843 ...  835 


Le  Roux  "  1857... 
Regnault  "  1871... 
Violle  "  1874... 


832 
792 
790 


It  is  not  necessary  for  the  purpose  of  this  elementary  treatise  to 
enter  into  an  investigation  of  what  is  the  true  equivalent  of  heat,  be- 
cause a  constant  equivalent  cannot  be  realized  in  the  working  of  a 
steam-engine  ;  for  which  reason  Ave  will  here  limit  ourselves  only  to 
the  operation  of  evaporating  water  into  steam,  and  its  transmission 
through  a  steam-engine  wTith  or  without  expansion. 

The  thermo-dynamic  equivalent  of  heat  is  the  ratio  obtained  by 
dividing  the  work  in  foot-pounds  by  the  number  of  units  of  heat 
which  performs  that  work. 

Formula  2,  §  6,  gives  the  work  of  evaporation  of  a  volume  of  water 
W,  under  a  steam-pressure  P,  without  expansion,  or 


H'  =  units  of  heat  per  cubic  foot  of  steam.     (See  Nystrom's  Pocket- 

Boole,  pages  400,  401.) 
J=  thermo-dynamic  equivalent  of  heat,  which  is  the  work  accom- 

plished per  unit  of  heat  expended. 
X=  grade  of  expansion  of  steam. 

The  heat  utilized  by  the  evaporation*  of  water  will  then  be 
H'  JF(  •$•-!),  which,  divided  into  the  work,  Formula  2,  gives  the 
equivalent, 


H' 


U4P 
H' 


THERMO-DYNAMICS.  31 

§  17.  The  column  J,  Table  II.,  is  calculated  by  this  formula,  and 
it  will  be  seen  that  the  equivalent  varies  with  the  steam-pressure. 

When  the  steam  is  expanded,  the  equivalent  will  be  increased  by 
the  hyperbolic  logarithm  of  the  expansion.  When  the  steam  is  ex- 
panded say  twice  its  volume,  then  X=  2,  for  which  the  hyperbolic 
logarithm  is  0.693,  or  69  per  cent,  is  gained  by  that  expansion  ;  there- 
fore the  gross  equivalent  realized  by  steam  working  expansively 
will  be 


From  this  formula  we  obtain  the  grade  of  expansion  required  for 
any  value  of  the  equivalent  J  —  namely, 


Example  5.  How  much  must  steam  of  pressure  P=100  pounds  to 
the  square  inch  be  expanded  in  order  to  realize  Joule's  equivalent 
,7=772? 

- 1  =  13.771. 


The  number  corresponding  to  this  logarithm  is  777830  —  that  is  to 
say,  the  steam  must  be  expanded  777830  times  its  primitive  volume 
in  order  to  realize  772  foot-pounds  per  unit  of  heat  ;  but  the  steam 
will  condense  to  water  and  freeze  to  ice  long  before  that  expansion 
is  reached,  showing  the  inapplicability  of  Joule's  equivalent  to 
dynamics  of  steam. 

By  the  new  steam  formulas  given  farther  on,  the  thermo-dynamic 
equivalent  is  constant,  51.5  foot-pounds  of  work  per  unit  of  heat  — 
that  is,  for  full  steam  ;  and  when  expanded,  the  equivalent  will  be 


This  is  probably  the  correct  thermo-dynamic  equivalent  of  heat  as 
realized  by  steam. 


32  STEAM  ENGINEERING. 


HORSE-POWER    OF   STEAM-BOILERS    BY    EVAPORATION. 

§  18.  Heretofore  it  has  been  the  custom  to  rate  the  power  or  steam- 
ing capacity  of  a  boiler  by  the  indicated  horse-power  transmitted  by 
the  steam-engine,  and  it  has  been  found  that  one  and  the  same  boiler, 
fired  under  equal  circumstances,  but  supplying  steam  to  different 
engines,  has  produced  widely  different  indicated  horse-power,  thus 
demonstrating  that  the  power  transmitted  by  the  engine  is  not  a  cor- 
rect measure  of  the  real  power  or  steaming  capacity  of  the  boiler. 
The  question  then  arose,  How  can  the  power  of  the  boiler  be  correctly 
determined  independent  of  the  working  of  the  engine  ? 

When  a  steam-user  orders  a  boiler  from  a  boiler-maker,  it  is  gen- 
erally specified  in  the  contract  what  power  the  boiler  must  generate ; 
but  when  finished  and  tried,  the  parties  concerned  do  not  agree  as  to 
what  is  the  correct  horse-power  of  the  boiler,  and  law-suits  have  thus 
been  instituted  and  unjust  verdicts  rendered  for  want  of  a  definite 
rule  by  which  to  settle  the  question  indisputably  and  satisfactorily  to 
both  parties. 

In  one  case  a  boiler-maker  contracted  to  furnish  three  boilers  of 
75  IP  each,  or  in  all  225  IP,  for  a  price  of  $40  per  horse-power,  or  in 
all  $9000;  but  on  trial,  only  from  100  to  130  IP  was  generated,  ac- 
cording to  indicator  diagrams  from  the  steam-engine. 

§  19.  The  steam-user,  finding  that  power  insufficient  for  his  work, 
declined  to  pay  the  full  price,  $9000,  had  the  boilers  taken  out  and 
replaced  by  new  ones  of  the  requisite  power,  furnished  by  another 
boiler-maker. 

The  first  boiler-maker  maintained  that  his  boilers  were  of  the 
requisite  power,  and  sued  the  steam-user  in  order  to  recover  the  full 
price,  $9000.  Several  experts  on  steam-boiler  performance  were 
called  as  witnesses,  and  the  trial  of  the  case  lasted  four  days,  most  of 
which  time  was  consumed  in  arguing  what  quantity  of  water  evap- 
orated per  hour  is  equivalent  to  one  horse-power;  but  none  of  the 
experts  appeared  to  understand  the  subject.  The  judge  remarked 
that  scientific  evidence  could  not  be  admitted  in  the  case,  and 
asked  if  there  was  any  reliable  authority  on  the  subject,  and  was 
answered  no. 

One  expert  witn ess  stated  that  the  boilers  evaporated  100  cubic  feet 
of  water  per  hour  under  a  steam-pressure  of  75  pounds  to  the  square 
inch,  but  could  not  state  how  much  horse-power  that  evaporation 
would  be  equivalent  to.  No  evidence  was  given  to  the  fact  that  the 
boilers  did  not  come  up  to  225  horse-power,  and  the  jury  rendered  a 
verdict  for  the  boiler-maker  to  receive  the  full  pay,  $9000. 


HORSE-POWER   OF  STEAM-BOILERS,  33 

The  evaporation  of  100  cubic  feet  of  water  per  hour  under  a  pres- 
sure of  75  pounds  to  the  square  inch  is  equivalent  to  160  IP,  and  the 
boilers  consequently  did  not  come  up  to  the  225  IP  contracted  for. 
Cases  of  this  kind  have  frequently  occurred  and  caused  much  incon- 
venience to  the  parties  concerned. 

The  horse-power  of  a  steam-boiler  can  be  determined  correctly  by 
the  quantity  of  water  evaporated  per  unit  of  time  independent  of  the 
working  of  the  steam-engine,  supposing  that  all  the  water  is  evapo- 
rated and  nothing  carried  over  in  the  form  of  foam,  known  as  priming. 
A  distinct  line  can  thus  be  traced  between  the  efficiencies  of  the  power- 
generator  and  the  motor. 

§  20.  The  horse-power  given  by  the  indicator  diagrams  depends  much 
upon  the  construction  of  the  engine,  the  regulation  of  the  steam- valves, 
the  grade  of  expansion  used  and  the  correctness  of  the  indicator,  with 
which  the  boiler-maker  has,  nothing  to  do,  and  for  which  the  perform- 
ance of  the  boiler  should  not  be  held  responsible. 

The  steam-engine  may  be  connected  with  the  boiler  by  a  long,  nar- 
row and  uncovered  steam-pipe,  in  which  steam  may  condense  by  ra- 
diation of  heat,  and  the  steam  cylinder  may  be  uncovered,  which 
reduces  the  indicated  horse-power. 

§  21.  A  condensing  or  compound  engine  working  with  a  high  de- 
gree of  expansion  indicates  much  more  power  per  water  evaporated 
than  does  a  non-condensing  engine  working  with  full  steam,  which 
difference  of  power  depends  upon  the  engine-builder,  and  not  upon  the 
boiler-maker. 

The  question  may  arise  whether  the  steam-pressure  of  the  horse- 
power should  be  taken  above  vacuum  or  above  the  atmospheric  pres- 
sure. The  boiler-maker  may  argue  that  the  steam  generated  in  his 
boiler  drives  out  the  atmospheric  pressure,  and  thus  claim  the  right 
to  be  credited  with  the  gross  power  of  the  steam  supplied  from  his 
boiler. 

The  steam-user,  on  the  other  hand,  cannot  realize  all»that  power 
for  his  work,  and  is  therefore  not  willing  to  pay  for  more  than  value 
received.  The  boiler-maker  does  not  undertake  to  remove  the  atmo- 
spheric pressure  from  the  back  side  of  the  cylinder-piston,  which  is 
partly  done  by  the  engine-builder  making  a  condensing  engine,  for 
which  the  power  of  the  boiler  should  include  only  the  pressure  indi- 
cated by  a  proper  steam-gauge  or  safety-valve,  which  is  the  pressure 
for  estimating  the  power  of  a  non-condensing  engine. 

§  22.  The  legal  horse-power  of  a  steam-boiler  fired  with  a  given 
kind  or  quality  of  fuel  should  therefore  be  that  passing  from  the 
boiler  into  the  steam-pipe,  with  the  pressure  above  that  of  the  at- 


34  STEAM  ENGINEERING. 

mosphere,  independent  of  the  indicated  power  transmitted  by  the 
steam-engine. 

When  a  water-owner  rents  out  a  waterfall,  he  only  furnishes  the 
natural  effect,  and  does  not  hold  himself  responsible  for  the  efficiency 
of  the  water-wheel  which  the  miller  may  employ  for  realizing  the 
power  of  that  fall.  It  is  to  the  interest  of  the  miller  to  use  the  best 
wheel  that  will  utilize  the  highest  percentage  of  the  definite  natural 
effect  of  the  waterfall. 

So  it  should  be  also  with  boilers  and  engines.  The  boiler-maker 
furnishes  a  steam-boiler  generating  a  definite  natural  effect  of  unex- 
panded  steam,  and  it  is  to  the  interest  of  the  steam-user  to  employ  the 
best  construction  of  engine  in  order  to  utilize  the  highest  percentage 
of  the  natural  effect  of  that  steam. 

The  price  of  a  steam-boiler  should  be  rated  according  to  the  natural 
effect  it  generates  with  a  given  quality  and  quantity  of  fuel  consumed 
per  unit  of  time,  and  the  boiler-maker  should  not  be  entitled  to  remu- 
neration for  the  effect  realized  by  the  superior  construction  of  the 
steam-engine,  which  credit  is  due  to  the  engine-builder,  who  is  paid 
therefor  by  the  steam-user. 

§  23.  The  legal  horse-power  of  a  steam-boiler  should  therefore  be 
that  determined  by  Formula  11,  §  7,  with  the  exception  that  the  steam- 
pressure  p  should  be  taken  above  that  of  the  atmosphere — namely, 


13748.4 

The  water  required  to  be  evaporated  per  hour  for  a  given  horse- 
power is 

w    13748.4  H> 


log.  13748.4  =  4.1382522. 
W=  cubic  feet  of  water  of  temperature  32°  Fahr.  evaporated  per 

hour. 
•^  =  steam-volume  compared  with  that  of  its  water  at  32°  Fahr. 

See  pages  400,  401,  Nystrom's  Pocket-Book. 

When  the  water  evaporated  per  hour  is  expressed  in  pounds,  the 
Formulas  1  and  2  will  be 


857721 

857721  IP 
—       - 

Xt-D 


HORSE-POWER   OF  STEAM-BOILERS.  35 


The  term  "legal"  is  used  on  the  ground  that  the  formulas  are 
based  upon  Watt's  unit  of  horse-power,  which  unit  is  legalized  all 
over  the  civilized  world,  differing  only  slightly  in  different  countries, 
to  accommodate  the  different  units  of  weight  and  measure  ;  therefore 
the  legalization  of  Watt's  rule  for  horse-power  makes  the  formulas  in 
this  paragraph  legal. 

Watt's  unit  for  horse-power  is  33000  minute-foot-pounds,  which  is 
the  same  as  550  second-foot-pounds,  the  standard  upon  which  the 
formulas  are  based. 

Example  3.  What  is  the  horse-power  of  a  boiler  evaporating 
fts.  =  640  pounds  of  water  per  hour  of  temperature  t  =  80°,  to  steam 
of  p  =  80  pounds  to  the  square  inch  ? 

640x80(280.5-1) 
857721 

Correction  for  temperature  of  feed-water  80°  will  be  0.9577  x  166.84 
=  159.78,  the  horse-power  required. 

Example  1.  A  steam-boiler  evaporating  TF=  64  cubic  feet  of  water 
per  hour,  under  a  pressure  of  p  =  85  pounds  to  the  square  inch  above 
that  of  the  atmosphere,  the  temperature  of  the  feed-water  being  t 
=  120°  Fahr.  Required  the  legal  horse-power  of  the  boiler? 


Correction  for  temperature  120°  of  the  feed-water  will  be,  see  Table 
I.,  page  22. 

IP  =  0.9199  x  105.57  =  97.113,  the  legal  horse-power  required. 

Example  2.  How  much  feed-water  of  t  =  90°  must  be  evaporated 
per  hour  under  a  pressure  of  p  =  65  pounds  to  the  square  inch  above 
that  of  the  atmosphere  in  order  to  generate  a  legal  horse-power 
IP  =  360  horses  of  the  boiler? 


Correction  for  temperature  t  -  90°  W=  232.8  :  0.9486  =  245.43  cubic 
feet,  the  quantity  of  water  required. 

The  following  Table  IV.  is  calculated  from  the  above  formulas, 
giving  the  quantity  of  water  expressed  in  cubic  feet,  cubic  inches  or 
pounds  required  to  be  evaporated  per  hour  per  horse-power,  and  also 
the  horse-power  per  cubic  foot  of  water  evaporated  per  hour  under 
different  pressures. 


36 


STEAM  ENGINEERING. 


TABLE  IV. 

Legal  Horse-power  of  Steam-boilers  per  Rate  of 

Evaporation  of  "Water  to  Steam. 

Steam 
pressure 
ab.  atm. 

Water  e 
Cubic  feet. 

/aporated  per 
horse-power 

Cubic  in. 

hour  per 
Pounds. 

Horse- 
power 
per  cub.  ft. 

Work, 
ft.-lbs.  per 
unit  of  heat. 

P 

w 

W 

Ibs. 

B? 

J 

5 

2.2562 

3898.8 

140.76 

0.4433 

12.225 

10 

1.3983 

2416.2 

87.235 

0.7150 

19.616 

15 

1.1106 

1919.0 

69.284 

0.9005 

24.701 

20 

0.9654 

1668.1 

60.226 

1.0358 

28.380 

25 

0.9770 

1515.4 

54.711 

1.1403 

31.145 

30 

0.8176 

1411.9 

51.010 

1.2231 

33.433 

35 

0.7743 

1338.1 

48.308 

1.2914 

35.171 

40 

0.7412 

1280.9 

46.244 

1.3490 

36.683 

45 

0.7150 

1235.5 

44.605 

1.3986 

37.988 

50 

0.6935 

1198.3 

43.264 

1.4420 

39.124 

55 

0.6755 

1167.2 

42.140 

1.4804 

40.118 

60 

0.6600 

1140.6 

41.180 

1.5150 

41.012 

65 

0.6467 

1117.5 

40.345 

1.5463 

41.819 

70 

0.6349 

1097.1 

39.607 

1.5750 

42.551 

75 

0.6243 

1078.9 

38.951 

1.6016 

43.221 

80 

0.6149 

1062.5 

38.360 

1.6263 

43.854 

85 

0.6062 

1046.6 

37.822 

1.6495 

44.425 

90 

0.5983 

1033.9 

37.328 

1.6713 

45.011 

95 

0.5910 

1021.3 

36.873 

1.6919 

45.533 

100 

0.5847 

1009.6 

36.451 

1.7115 

46.027 

105 

0.5779 

998.67 

36.056 

1.7303 

46.495 

110 

0.5720 

988.44 

35.686 

1.7482 

46.949 

115 

0.5664 

978.75 

35.337 

1.7655 

47.390 

120 

"  0.5611 

969.62 

35.007 

1.7822 

47.812 

125 

0.5561 

960.96 

34.694 

1.7982 

48.213 

130 

0.5513 

952.65 

34.394 

1.8073 

48.604 

135 

0.5468 

945.00 

34.111 

1.8288 

49.737 

HOESE-POWER   OF  STEAM-BOILERS.  37 

HORSE-POWER    OF    STEAM-BOILERS    BY    FIRE-GRATE    AND 
HEATING    SURFACE. 

§  24.  The  evaporating  capacity  of  a  steam-boiler  fired  with  a  given 
kind  or  quality  of  fuel  depends  upon  the  extent  of  area  of  fire-grate 
and  heating  surface. 

B  =  area  of  fire-grate  in  square  feet. 

Q  =  heating  surface  in  square  feet. 

W=  cubic  feet  of  water  of  temperature  32°  Fahr.  evaporated  per 
hour. 

In  ordinary  steam-boilers  the  average  evaporation  with  natural 
draft  is 

TF=0.41/B~a,     ....        1 

under  the  condition  that  the  heating  surface  should  be  between  18 
and  36  times  the  area  of  the  fire-grate. 

This  water,  multiplied  by  the  steam-volume,  gives  the  space  gen- 
erated per  hour  by  the  steam,  or 


>Sr=0.4(^-l)1/B  a,        ...        2 

S  =  cubic  feet  of  steam  generated  per  hour. 

This  space,  multiplied  by  the  steam-pressure  per  square  foot  144  P, 
gives  the  work  accomplished  by  the  steam  per  hour. 


..        3 
K=  57.6  P(ir-  l)i/Bfa     ...        4 

This  work,  divided  by  33,000  pounds  times  60  minutes  =  1,980,000, 
gives  the  horse-power  of  the  boiler  expressed  by  area  of  fire-grate  and 
heating  surface. 


1980000 


34400 

This  formula  gives  the  gross  effect  or  horse-power  of  the  steam 
above  vacuum  ;  but  for  the  practical  rating  of  the  power  of  a  steam- 
boiler,  the  pressure  should  be  taken  above  that  of  the  atmosphere,  or 


34400 


38  STEAM  ENGINEERING. 

§  25.  Although  thi.s  formula  gives  the  average  horse-power  of  a 
steam-boiler,  it  cannot  be  termed  legal  because  the  evaporation  is 
the  real  power  of  the  boiler,  which  depends  upon  the  firing,  circula- 
tion of  water  and  other  variable  circumstances  not  included  in  the 
formula. 

The  volume  ("^  —  1)  varies  inversely  with  the  pressure,  and  the 
product^  (ft  - 1)  varies  nearly  as  the  cube  root  of  the  pressure  p,  for 
which  we  may  practically  place  p  (^  - 1)  =  5000  y'p,  and  the  horse- 
power of  the  boiler  will  be  for  a  chimney  50  feet  high, 

xlr  —  .          •  ,  •  •  o 

See  Table  of  Corrections  for  Height  of  Chimney. 

This  formula  should  not  be  used  for  less  pressure  than  p  =  15 
pounds  to  the  square  inch. 

Example  8.  Required  the  horse-power  of  a  steam-boiler  with  fire- 
grate B  =  130  square  feet,  and  heating-surface  L3  =  3372  square  feet, 
carrying  a  steam-pressure  of  p  =  50  pounds  to  the  square  inch  above 
that  of  the  atmosphere  ? 

,     1^50/130x3372 

Formula  42.     IP  =  *-    •x— =  354.53  horse-power. 

6.88 

This  is  the  horse-power  the  boiler  would  generate  without  expand- 
ing the  steam. 

Example  1.  Required  the  quantity  of  water  evaporated  per  hour 
by  the  fire-grate  B  =  130,  and  heating-surface  O  =  3372  square  feet? 

Formula  1.     W=  0.4/130x3372  =  264.8  cubic  feet. 

The  efficiencies  of  steam-boilers  can  readily  be  compared  with  these 
formulas. 

When  the  steam  is  expanded  in  the  engine,  the  power  derived  from 
the  boiler  may  practically  be  estimated  as  follows : 


This  formula  should  not  be  taken  for  the  horse-power  of  the  steam- 
boiler,  but  for  that  transmitted  by  the  engine. 

In  the  preceding  example  we  have  the  horse-power  IP  =  354.53 
when  working  with  full  steam ;  but  if  the  steam  is  expanded  say 
X=B  times,  we  have  hyp.log.B  =  1.0986  and  2.0986x354.53  =  744 


HORSE-POWER  OF  STEAM-BOILERS. 


39 


horse-power,  of  which  70  per  cent,  may  be  transmitted  through  the 
engine,  or 

IP  =  744  x  0.7  -  520.8  horse-power, 

which  would  probably  be  indicated  by  diagrams. 

It  is  supposed  in  the  preceding  examples  that  the  temperature  of 
the  feed-water  is  32°.  For  any  other  temperature  up  to  212°,  use 
the  correction  in  the  following  Table  V.,  corresponding  to  the  actual 
temperature  of  the  feed-water,  as  follows : 

R  =  correction  in  the  Table  V. 


H> 


6.88 


TABLE   V. 

Gain  of  Power  or  Water  evaporated  by  heating  the 
Feed-water  from  32°  to  t. 


Temp.  t. 

Gain  R. 

Logarithm. 

Temp.  t. 

Gain  R. 

Logarithm. 

40 

1.0068 

0.0029432 

130 

1.0983 

0.0407210 

sa 

1.0151 

0.0065088 

140 

1.1111 

0.0457531 

60 

1.0245 

0.0105120 

150 

1.1221 

0.0500316 

70 

1.0340 

0.0145205 

160 

1.1344 

0.0547662 

80 

1.0441 

0.0187421 

170 

1.1469 

0.0595256 

90 

1.0542 

0.0229230 

180 

1.1594 

0.0642333 

100 

1.0647 

0.0272273 

190 

1.1725 

0.0691129 

110 

1.0757 

0.0316912 

200 

1.1859 

0.0740481 

120 

1.0870 

0.0362295 

212 

1.2023 

0.0800128 

The  horse-power  given  by  Formulas  8,  multiplied  by  the  correction 
for  height  of  chimney,  Table  VII. ,  gives  the  horse-power  which  may 
be  expected  from  the  boiler. 

The  following  Table  VI.  gives  the  horse-power  of  boilers  per  square 
foot  of  grate-surface  for  different  proportions  of  heating-surface,  when 
the  steam  is  worked  without  expansion  through  a  non-condensing 
engine,  and  the  temperature  of  the  feed-water  is  32°. 


40 


STEAM  ENGINEERING. 


TABLE  VI. 

Horse-power  per  Square  Foot  of  Fire-grate  for  Chimney 
50  Feet  High. 

Steam 
pressure. 

a  =  i6B 

Proportion  of  flre-gr 

a  =  20  B    a  =  25  B 

ate  and  heal 

a  =  30B 

ing  surface. 

a  =  35B 

a=4oB 

P 

IP 

IP 

IP 

IP 

IP 

IP 

25 

1.7 

1.91 

2.14 

2.33 

2.52 

2.63 

30 

1.81 

2.02 

2.27 

2.48 

2.67 

2.8 

35 

1.91 

2.13 

2.38 

2.61 

2.81 

2.95 

40 

2. 

2.23 

2.49 

2.73 

2.94 

3.08 

45 

2.08 

2.32 

2.59 

2.84 

3.06 

3.2 

50 

2.15 

2.4 

2.68 

2.94 

3.17 

3.32 

55 

2.22 

2.48 

2.77 

3.03 

3.28 

3.42 

60 

2.29 

2.55 

2.85    ' 

3.12 

3.37 

3.52 

65 

2.35 

3.62 

2.93 

3.2 

3.46 

3.62 

70 

2.4 

3.67' 

2.99 

3.27 

3.53 

3.7 

75 

2.46 

2.74 

3.07 

3.36 

3.63 

3.8 

80 

2.51 

2.81 

3.13 

3.43 

3.71 

3.88 

85 

2.57 

2.87 

3.2 

3.51 

3.79 

3.96 

90 

2.62 

2.92 

3.26 

3.57 

3.85 

4.04 

95 

2.66 

2.97 

3.32 

3.63 

3.93 

4.11 

100 

2.71 

3.02 

3.38 

3.7 

4. 

4.19 

110 

2.8 

3.12 

3.49 

3.82 

4.13 

4.32 

120 

2.88 

3.21 

3.59 

3.93 

4.24 

4.44 

130 

2.96 

3.3 

3.68 

4.04 

4.36 

4.57 

140 

3.03 

3.38 

3.78 

4.14 

4.47 

4.68 

150 

3.11 

3.46 

3.87 

4.23 

4.57 

4.79 

160 

3.17 

3.54 

3.95 

4.33 

4.67 

4.89 

170 

3.23 

3.62 

4.03 

4.42 

4.77 

4.99 

180 

3.3 

3.68 

4.11 

4.5 

4.86 

5.09 

190 

3.36 

3.74 

4.21 

4.58 

4.94 

5.18 

200 

3.41 

3.81 

4.26 

4.64 

5.03 

5.27 

210 

3.47 

3.88 

4.32 

4.74 

5.11 

5.36 

220 

3.52 

3.93 

4.39 

4.81 

5.2 

5.44 

230 

3.58 

3.99 

4.46 

4.88 

5.28 

5.52 

240 

3.63 

4.05 

4.52 

4.95 

5.35 

5.6 

250 

3.68 

4.11 

4.59 

5.03 

5.42 

5.68 

260 

3.72 

4.16 

4.65 

5.09 

5.49 

5.75 

270 

3.77 

4.21 

4.70 

5.16 

5.57 

5.82 

280 

3.82 

4.26 

4.76 

5.22 

5.63 

5.9 

290 

3.87 

4.31 

4.82 

5.28 

5.69 

5.96 

300 

3.9 

4.36 

4.87 

5.34 

5.75' 

6.03 

i 

HEIGHT  OF  CHIMNEYS. 


41 


TABLE  VII. 

Correction  of  Horse-power  per  Square  Foot  of  Grate  for 
Different  Heights  of  Chimneys  in  Feet. 


Height 
Chim- 
ney. 

Correc- 
tion. 

Height 
Chimney. 

Correc- 
tion. 

Height 
Chimney. 

Correc- 
tion. 

Height 
Chimney. 

Correc- 
tion. 

feet. 

r. 

feet. 

r. 

feet. 

r. 

feet. 

r. 

10 

0.5 

75 

1.20 

180 

1.78 

310 

2.27 

15 

0.59 

80 

1.23 

190 

1.82 

320 

2.30 

20 

0.67 

85 

1.27 

200 

1.86 

330 

2.33 

25 

0.74 

90 

1.30 

210 

1.90 

340 

2.36 

30 

0.8 

95 

1.33 

220 

1.94 

350 

2.40 

35 

0.85 

100 

1.36 

230 

1.98 

360 

2.43 

40 

0.91 

110 

1.42 

240 

2.02 

370 

2.46 

45 

0.96 

120 

1.48 

250 

2.06 

380 

2.49 

50 

1.00 

•   130 

1.53 

260 

2.10 

390 

2.52 

55 

1.04 

140 

.   1.58 

270 

2.13 

400 

2.55 

60 

1.08 

150 

1.63 

280 

2.16 

410 

2.57 

65 

1.12 

160 

1.68 

290 

2.20 

420 

2.60 

70 

1.16 

170 

1.73 

300 

2.23 

430 

2.63 

Allowance  is  made  in  the  above  table  for  radiation  or  conduction 
of  heat  from  the  gases  through  the  walls  of  the  chimney. 

TABLE  VIII. 

Consumption  of  Coal  in  Pounds  per  Hour  per  Square  Foot 
of  Grate,  for  Different  Heights  of  Chimney. 


Height 
Chim- 
ney. 

Consunipt. 
coal. 

Height 
Chimney. 

Consumpt. 
coal. 

Height 
Chimney. 

Consumpt. 
coal. 

Height 
Chimney. 

Consumpt. 
coal. 

10 

7.00 

75 

16.8 

180 

25. 

310 

31.8 

15 

8.25 

80 

17.2 

190 

25.5 

320 

32.2 

20 

9.4 

85 

17.8 

200 

26. 

330 

32.7 

25 

10.4 

90 

18.2 

210 

26.5 

340 

33.1 

30 

11.2 

95 

18.6 

220 

27.2 

350 

33.6 

35 

12. 

100 

19. 

230 

27.7 

360 

34. 

40 

12.8 

110 

19.9 

240 

28.3 

370 

34.4 

45 

13.4 

120 

20.7 

250 

28.9 

380 

34.9 

50 

14. 

130 

21.4 

260 

29.4 

390 

35.3 

55 

14.6 

140 

22.1 

270 

29.8 

400 

35.7 

60 

15.1 

150 

22.9 

280 

30.3 

410 

36. 

65 

15.7 

160 

23.5 

290 

30.8 

420 

36.4 

70 

16.2 

170 

24.2 

300 

31.2 

430 

36.8 

It  is  not  expected  that  this  gives  the  correct  consumption  of  coal, 
which  depends  much  upon  the  kind  of  coal  and  manner  of  firing, 
but  it  gives  the  proportionate  consumption  to  the  height  of  the 
chimney.  See  horse-power  of  chimney,  Table  XXIX.,  page  123. 


42  STEAM  ENGINEERING. 

CHIMNEYS. 

§  26.  The  proportion  of  a  chimney  to  the  horse-power  of  the  steam 
generated  and  consumption  of  fuel  on  the  fire-grate  is  a  very  difficult 
problem  to  solve  theoretically.  It  is  certain,  however,  that  the  horse- 
power of  a  chimney,  as  well  as  the  consumption  of  fuel  on  the  fire- 
grate, is  directly  as  the  section  area  and  square  root  of  the  height  of 
the  chimney. 

The  term  "horse-power"  in  this  connection  means  the  power  of 
draft  in  a  chimney  required  for  the  combustion  generating  heat  for 
evaporation  of  water  to  steam  of  a  given  horse-power. 

The  following  formulas  are  derived  from  both  theory  and  prac- 
tice, and  the  horse-power  is  that  generated  by  full  steam  without  ex- 
pansion : 

IP  =  horse-power  of  chimney. 

B  =  area  of  fire-grate  in  square  feet. 

A  =  section  area  of  chimney  in  square  feet. 

jET=  height  of  chimney  in  feet  when  A  =  0.16  B. 
C  =  pounds  of  coal  consumed  per  hour  on  the  fire-grate. 
r  =  coefficient  for  correction  in  the  preceding  Table  VII. 

Horse-power,  IP  =  10Ar 1 

Consumption  of  fuel,         C=14Br 2 

Area  of  chimney, 

Area  of  grate,  B  =  — 4 

14  r 

-rr> 

Correction,  r  =  — 5 

1U  A. 

C1 
Correction,  r  = .        .  6 

n         .- 
Correction, 

10.755 

Example  1.  Required  the  horse-pOAver  of  a  chimney  -H"=80  feet 
high  above  grate  and  A  =  4  square  feet  cross-section  ? 
Correction  for  80  feet  =  1.23. 

IP  =  10x4xl.23  =  49.2  horse-power. 


POWER   OF  COMBUSTION.  43 

Example  2.  How  much  coal  will  be  consumed  per  hour  on  a  fire- 
grate B  =  150  square  feet  connected  with  a  chimney  H  =  60  feet  high? 

Correction  for  60  feet  is  1.09. 

(7=  14  x  150  x  1.09  =  2289  pounds. 

Example  6.  What  height  of  chimney  is  required  for  a  draft  con- 
suming (7=1216  pounds  of  coal  per  hour  on  a  grate  E3  =  64  square 
feet? 

Correction,  r  =  —     —  —  1.357. 

14x64 

The  height  of  chimney  in  the  table  corresponding  to  this  correction 
is  H=  100  feet. 

Example  5.  A  chimney  is  to  be  constructed  for  a  boiler  having  a 
grate  surface  of  B  =  48  square  feet.  The  section  area  of  the  chimney 
is.  made  A  =  0.16  B  =  0.16  x  48  =  7.68  square  feet.  How  high  must  the 
chimney  be  that  the  draft'will  generate  IP  =  192  horse-power? 

192 
Correction,  r  = =  2.5.     Height  H=  390  feet. 

J.U  x  /  .00 

The  smoke-stacks  for  steamboats  are  generally  made  cylindrical  or 
parallel — that  is,  of  equal  section  from  boiler  to  top ;  but  brick  chim- 
neys for  factories  are  generally  made  taper,  with  about  45  per  cent, 
more  section  area  at  the  bottom  than  at  the  top.  The  area  A  in  the 
preceding  formulas  and  examples  should  be  that  at  the  top  of  the 
chimney. 

POWER    OF   COMBUSTION. 

§  27.  On  account  of  the  physical  constitution  of  heat  not  being  well 
understood,  an  intelligent  explanation  of  dynamics  of  combustion 
cannot  be  given. 

Combustion  is  the  operation  of  combining  oxygen  with  fuel,  which 
generates  heat ;  and  the  more  rapidly  that  combination  is  performed, 
the  higher  will  be  the  temperature  of  the  heat. 

The  chemical  combination  of  oxygen  with  a  definite  weight  of  fuel 
generates  a  definite  quantity  of  heat,  which  is  convertible  into  work, 
or  the  product  of  the  three  simple  physical  elements  force,  velocity 
and  time,  represented  by  F  V  T.  Of  this  work,  the  thermo-dynamic 
equivalents  may  be  represented  as  follows : 

F=  force,  which  is  convertible  into  temperature  of  the  heat, 
V=  velocity,  or  rate  of  combustion,  which  is  proportioned  to  the 

area  of  the  fire-grate. 

FV*=  power,  the  act  of  combustion,  or  combination  of  oxygen 
and  fuel. 


44  STEAM  ENGINEERING. 

V  T=  space,  or  the  volume  occupied  by  the  heat. 
FVT=  work,  which  represents  the  quantity  of  heat  generated  by  the 
combustion  in  the  time  T. 

For  a  definite  quantity  of  heat  generated  in  a  long  time  T  the 
power  F  V  must  be  small,  and  for  a  short  time  T  the  power  F  V 
must  be  larger ;  but  for  a  constant  power  F  V  either  one  of  the  ele- 
ments F  and  V  may  vary  at  the  expense  of  the  other. 

§  29.  For  a  definite  quantity  of  fuel  consumed  per  unit  of  time  on 
different  extent  of  grate-surface,  the  temperature  of  combustion  should 
be  inversely  as  the  grate-surface — that  is  to  say,  a  forced  draft  should 
generate  a  higher  temperature  of  the  fire  than  would  be  attained  by 
natural  draft. 

The  combustion  per  unit  of  time  is  as  the  square  root  of  the  pressure 
of  the  air. 

The  fuels  generally  used  for  generating  heat  are  carbon,  hydrogen 
and  sulphur,  of  which  only  carbon,  which  is  the  predominant  fuel 
used  in  steam-boilers,  will  herein  be  considered.  Carbon  forms  two 
compounds  with  oxygen — namely,  carbonic  oxide  G  0,  and  carbonic 
acid  C  02,  the  equivalent  of  carbon  being  6,  and  that  of  oxygen  8 — 
that  is  to  say,  6  pounds  of  carbon  united  with  8  pounds  of  oxygen 
forms  carbonic  oxide,  which  is  a  transparent,  colorless  gas  which 
when  ignited  will  burn  with  a  faint  flame,  taking  up  another  atom 
of  oxygen,  and  forms  carbonic  acid,  composed  of  6  pounds  of  carbon 
and  8x2  =  16  pounds  of  oxygen. 

One  pound  of  carbon  combined  with  16  :  6  =  2f  pounds  of  oxygen 
forms  31  pounds  of  carbonic  acid,  which  is  complete  combustion  of 
the  carbon. 

AIR    FOR   COMBUSTION. 

§  30.  The  oxygen  required  for  combustion  is  supplied  from  at- 
mospheric air,  which  is  a  mechanical  mixture  of 

23  weights  of  oxygen  to  77  of  nitrogen  in  100  weights  of  air. 

21  volumes  of  oxygen  to  79  of  nitrogen  in  100  volumes  of  air. 

One  cubic  foot  of  dry  atmospheric  air,  of  temperature  60°  Fahr. 
and  under  a  pressure  of  30  inches  of  mercury,  weighs  532  grains,  or 
0.076  of  a  pound,  and  13.158  cubic  feet  weighs  one  pound. 

One  pound  of  air  contains  0.23  pounds  of  oxygen,  and  13.158  :  0.23 
=  57.21  cubic  feet  of  air  to  make  one  pound  of  oxygen. 

The  combustion  of  one  pound  of  carbon  requires  2$  pounds  of  oxy- 
gen ;  therefore  57.21  x  21  =  152.56  cubic  feet  of  dry  air,  of  temperature 
60°,  is  required  for  the  complete  combustion  of  one  pound  of  carbon. 


TEMPERATURE  OF  DRAFT. 


45 


Carbonic  oxide  requires  57.21  xlj  =  76.28  cubic  feet  of  air  per 
pound  of  carbon  consumed. 

Different  temperatures  of  the  air  require  different  volumes  for  the 
combustion  of  one  pound  of  carbon,  as  shown  in  the  accompanying 
Table  IX. 

TABLE  IX. 
Properties  of  Air  for  Combustion. 


Temp, 
of  air. 
Fahr. 

Volume 
of  air. 
1  at  32°. 

Weight  per 
cub.  foot. 

v 

C 

1  Ib.  of 
air. 

ubic  feet  of 

1  Ib.  of 
oxygen. 

air  required 
Comb.  1  11 
carb.  acid. 

for 

).  carbon, 
carb.  oxide. 

10 

0.9554 

0.08414 

11.885 

51.674 

137.804 

68.902 

20 

0.9756 

-  0.08236 

12.142 

52.792 

140.778 

70.389 

'    32 

1.0000 

0.08023 

12.464 

54.191 

144.510 

72.255 

40 

1.0162 

0.07886 

12.681 

55.135 

147.026 

73.513 

50 

1.0365 

0.07718 

12957 

56.335 

150.226 

75.113 

60 

1.0567 

0.07600 

13.158 

57.209 

152.556 

76.278 

70 

1.0760 

0.07453 

13.417 

58.335 

155.560 

77.780 

80 

1.0973 

0.07311 

13.678 

59.470 

158.586 

79.293 

90 

1.1176 

0.07146 

13.994 

60.843 

162.248 

81.124 

100 

1.1378 

0.07051 

14.182 

61.661 

164.430 

82.215 

110 

1.1581 

0.06928 

14.434 

62.756 

167.348 

83.674 

120 

1.1784 

0.06808 

14.688 

63.861 

170.296 

85.148 

TEMPERATURE   OF   DRAFT. 

§  31.  In  comparative  experiments  on  evaporation  or  steaming 
capacities  of  boilers  supplied  with  air  of  widely  different  tempera- 
tures, various  opinions  have  been  advanced  as  to  what  would  be  the 
proper  allowance  for  temperature  of  the  air. 

When  the  air  of  different  temperatures  enters  the  furnace  under 
constant  pressure  or  natural  draft,  what  is  gained  by  the  warmer  air 
is  lost  by  less  oxygen  per  volume. 

In  a  cold  atmosphere  there  is  better  draft  in  the  chimney  than  in 
warmer  air ;  but  when  the  air  is  supplied  and  heated  under  pressure, 
as  in  a  blast-furnace,  then  there  is  an  advantage  in  the  combustion 
by  the  hot  air. 

In  a  cold  atmosphere  more  heat  will  no  doubt  be  radiated  from  the 
boiler  and  steam-pipe,  but  the  generation  of  heat  in  the  furnace  and 
steam  in  the  boiler  will  not  be  materially  diminished,  although  the 
cold  air  enters  the  fire  with  less  velocity  than  does  warmer  air. 


46  STEAM  ENGINEERING. 

HEAT   OF   COMBUSTION. 

§  81.  The  heat  of  combustion  means  the  quantity  of  heat  generated 
by  the  burning  of  a  given  weight  of  fuel,  and  which  is  a  distinct  quan- 
tity from  that  of  the  temperature  of  the  fire. 

The  English  unit  of  heat  is  that  required  to  elevate  the  temperature 
of  one  pound  of  water  from  39°  to  40°  Fahr.  The  experiments  of 
Regnault  show  that  the  elevation  of  the  temperature  of  one  pound  of 
water  from  32°  to  212°  or  180°  requires  180.9  units  of  heat — that  is 
to  say,  for  higher  temperatures  than  39°  to  40°  it  requires  a  little 
more  than  one  unit  of  heat  to  elevate  the  temperature  of  one  pound 
of  water  one  degree ;  but  the  difference  is  so  small  that  in  practice  we 
may  consider  one  unit  of  heat  as  standard  for  elevating  the  tempera- 
ture of  one  pound  of  water  one  degree  at  all  temperatures  below  that 
of  the  boiling  point. 

The  experiments  of  Favre  and  Silberman  show  that  the  combus- 
tion of  one  pound  of  carbon  to  2&  pounds  of  carbonic  oxide  generates 
4400  units  of  heat,  and  to  2f  pounds  of  carbonic  acid  14,500  units  of 
heat.  That  is  to  say,  the  acid  generates  14,500  :  4400  =  3.27  times 
more  heat  than  does  the  oxide,  showing  the  importance  of  burning 
the  fuel  completely  to  acid.  If  it  requires,  say,  150  cubic  feet  of  air 
for  burning  one  pound  of  carbon  to  acid,  it  requires  only  75  cubic 
feet  for  the  burning  to  oxide.  Now,  if  the  supply  of  air  is  between 
150  and  75  cubic  feet,  both  the  gases  will  be  formed  and  mechanically 
mixed,  but  not  chemically  combined,  in  the  combustion  chamber. 

Suppose  120  cubic  feet  of  air  is  supplied  per  pound  of  carbon 
consumed,  what  will  be  the  proportion  of  oxide  and  acid  formed? 
and  how  many  units  of  keat  will  be  generated  per  pound  of  carbon 
consumed  ? 

Assuming  the  temperature  of  the  air  to  be  60°,  it  requires  57.21 
cubic  feet  to  make  one  pound  of  oxygen,  and  120  :  57.21  =  2.0975,  say 
two  pounds  of  oxygen. 

56  —  21  x  2 
Carbonic  oxide  = ' =  1.1666  pounds. 

oo  x  o  —  44 
Carbonic  acid    = —          —  =  1.8333  pounds. 

One  pound  of  carbonic  oxide  generates  1650  units  of  heat.  One 
pound  of  carbonic  acid  generates  3960  units  of  heat.  Then  1650 
x  1.1666  +  3960  x  1.8333  =  9184.75  units  of  heat  generated  by  the  com- 
bustion of  one  pound  of  carbon  with  the  oxygen  of  120  cubic  feet  of 
air.  With  30  cubic  feet,  or  25  per  cent.,  more  air  the  carbon  would 


FORMULAS  FOR  HEAT  AND   COMBUSTION. 


47 


have  been  consumed  to  acid,  and  generated  14,500,  or  nearly  58  per 
cent,  more  heat.  This  shows  the  importance  of  supplying  a  sufficient 
quantity  of  air  to  the  furnace  for  the  complete  combustion  of  the 
carbon  to  carbonic  acid. 

2  32.  FORMULAS  FOR  HEAT  AND  COMBUSTION. 

CO  =  pounds  of  carbonic  oxide,  "I 

CO,  =  pounds  of  carbonic  acid,    /  formed  b^  combustlOD- 
(7=  pounds  of  carbon  consumed  by 
0  =  pound  of  oxygen. 
h  =  units  of  heat  generated  by  the  combustion. 

56  (7-21  0 


C0  = 


C0,- 


12 

33  0-44  C 
12 


7i  =  3960 (CO,)  +  1650 (CO)    ...        3 

The  following  Table  X.  is  calculated  by  the  above  formulas,  making 
C=  1  pound  of  carbon.  The  first  column  contains  the  oxygen  sup- 
plied for  the  combustion  of  one  pound  of  carbon,  and  the  second  col- 
umn the  cubic  feet  of  air  containing  the  oxygen  in  the  first  column : 


TABLE  X. 
Operation  of  Incomplete  Combustion  of  Carbon. 


Per  Ib.  of 
Oxygen 
Ibs. 

Carbon. 
Air  60° 
cub.  feet. 

Carbon! 
CO  Ibs. 

:  Oxide. 
Units  of 
heat. 

Carbon 
C02  Ibs. 

c  Acid. 
Units  of 
heat. 

Total 
units  of 
heat. 

Percent- 
age of 
heat  lost. 

U 

76.278 

2i 

4400 

0 

0 

4400 

69.65 

1.4 

80.092 

2.2222 

3666.6 

0.1833 

726.0 

4713.6 

67.02 

1.5 

85.813 

2.0416 

3368.6 

0.4583 

1813.4 

5182.0 

64.26 

1.6 

'91.534 

1.8666 

3080.0 

0.7333 

2904.0 

5984.0 

58.73 

1.7 

97.265 

1.6916 

2791.3 

0.9258 

3666.1 

6457.4 

55.47 

1.8 

102.99 

1.5166 

2502.5 

1.2833 

5082.0 

7584.5 

47.69 

1.9 

108.71 

1.3416 

2213.8 

1.5583 

6169.7 

8382.5 

42.19 

2.0 

114.42 

1.1666 

1925.0 

1.8333 

7260.0 

9185.0 

36.66 

2.1 

120.14 

0.9916 

1636.3 

2.1083 

8349.0 

9985.3 

31.14 

2.2 

125.86 

0.8166 

1347.5 

2.3833 

9438.0 

10785 

25.62 

2.3 

131.58 

0.6416 

1058.8 

2.6583 

10527 

11586 

20.10 

2.4 

137.30 

0.4666 

770.0 

2.9333 

11616 

12386 

14.58 

2.5 

143.02 

0.2916 

481.3 

3.2083 

12705 

13186 

9.06 

M 

152.55 

0.0000 

0000 

3.6666 

14500 

14500 

0.00 

48  STEAM  ENGINEERING. 

Suppose  120.14  cubic  feet  of  air  is  supplied  per  pound  of  carbon  con- 
sumed, the  results  will  be  as  in  the  table — namely. 

Carbonic  oxide          CO  =  0.9916  Ibs.  of  1636.3  units  of  heat. 

Carbonic  acid  CO.,  =  2.1083  Ibs.  of  8349.    units  of  heat. 

Products  of  combustion  =  3.0999  fts.  of  9985.3  units  of  heat. 

The  loss  by  incomplete  combustion  is  31.14  per  cent.,  as  shown  in 
the  last  column  of  the  table. 

This  table  shows  the  operation  of  incomplete  combustion  with  a  dif- 
ferent supply  of  air  per  pound  of  carbon  consumed.  For  instance, 
if  114.42  cubic  feet  of  air  is  supplied  per  pound  of  carbon  consumed, 
it  will  generate  1.16  pounds  of  CO  of  1925  units  of  heat  and  1.83 
pounds  of  CO,  of  7260  units  of  heat ;  in  all  9185  units  of  heat,  with 
36.6  per  cent,  loss  of  that  if  152.55  cubic  feet  of  air  had  been  supplied. 

When  less  air  is  supplied  than  is  required  for  forming  carbonic  a'cid, 
the  produce  of  combustion  will  form  smoke  with  unconsumed  particles 
of  carbon ;  and  when  more  air  is  supplied  than  is  required  for  forming 
carbonic  acid,  the  excess  will  be  heated  by  the  products  of  combus- 
tion, which  heat  is  thus  lost  and  carried  up  through  the  chimney. 


FUEL. 

§  33.  The  fuels  generally  used  in  steam-boilers  for  combustion  to 
generate  heat  are  wood,  charcoal,  peat,  mineral  coal  and  coke,  none  of 
which  is  pure  carbon,  as  heretofore  assumed  in  the  operation  of  com- 
bustion, but  contains  various  proportions  of  carbon,  hydrogen,  oxygen 
and  involatilizable  matter  forming  ash.  The  hydrogen  in  the  fuel, 
combined  with  oxygen  by  combustion,  generates  about  four  times  as 
much  heat  per  weight  of  hydrogen  consumed  as  does  an  equal  weight 
of  carbon.  The  combustion  of  one  pound  of  hydrogen  by  8  pounds 
of  oxygen  forms  steam  and  generates  62032  units  of  heat;  there- 
fore, if  one  pound  of  fuel  contains,  say  0.9  of  a  pound  of  carbon  and 
0.1  of  a  pound  of  hydrogen,  the  heat  generated  by  the  combustion 
will  be 

Hydrogen,  62032  x  0.1  =   6203.2  units  of  heat. 
Carbon,       14500  x  Q.9  - 13050        " 

Total,     =  19253.2  units  of  heat. 

When  the  fuel  contains  only  carbon  and  hydrogen,  the  following 
forms  for  combustion  give  the  units  of  heat  generated : 

a  =  fraction  of  carbon      j  ^  Qne          d  of  ^ 
H'  -       "  hydrogen ) 


MOISTURE  IN  FUEL.  49 

0  =  pounds  of  oxygen  required  for  the  complete  combustion  per 
pound  of  fuel. 


A  =  cubic  feet  of  air  at  60°  required  for  the  combustion  of  one 
pound  of  fuel. 


The  units  of  heat  generated  per  pound  of  fuel  consumed  will  be 
A  =  62032IP  + 145000'      ...        3 

MOISTURE    IN    FUEL. 

§  34.  When  a  fuel  contains  both  oxygen  and  hydrogen  partly  com- 
bined in  the  form  of  water  or  moisture,  that  part  of  the  fuel  will  be 
inert  in  the  generation  of  heat.  One-eighth  of  the  oxygen  will  be 
eqtfal  to  the  inert  part  of  the  hydrogen,  so  that  the  heat  generated 

by  the  hydrogen  in  the  fuel  will  be  h  =  62030 (if'  -  — )         .        4 

\  8/ 

Heat  by  the  carbon,  h  =  145000'    ...        5 
The  sum  of  these  two  formulas  will  be  the  heat  generated  by  the 
fuel  when  sufficient  oxygen  is  supplied  for  its  combustion — namely, 

h  =  1 4500 1  C'  +  4.28(5"'  -  —  |  6 


fc" +4.28(5"'- 


C' ,  H'  and  O  are  fractions  in  one  pound  of  the  fuel. 
The  weight  of  oxygen  required  for  this  combustion  will  be 


The  cubic  feet  of  air  of  60°  required  for  this  oxygen  is 
A=l 


UNCOMBINED  OXYGEN  AND  HYDROGEN  IN  FUEL. 

§  35.  When  the  oxygen  and  hydrogen  in  a  fuel  are  not  chemically 
combined,  their  combination  by  combustion  will  generate  heat,  and 
the  oxygen  required  for  the  combustion  of  the  C'  and  H'  will  be 
diminished  by  (7. 

When  a  fuel  contains  the  three  combustibles  carbon,  hydrogen  and 
sulphur,  the  heat  generated  by  its  complete  combustion  will  be 

h  =  14500  C'  +  620305"' +  4032S'        .        .        9 

4 


50 


STEAM  ENGINEERING. 


The  proportion  of  ingredients  in  fuel  varies  very  much,  even  in  the 
same  kind  of  fuel  like  mineral  coal,  for  which  analyses  and  experiments 
must  be  made  with  each  fuel  to  determine  its  correct  heating  power. 

The  following  Table  XI.  gives  the  average  proportion  and  property 
of  different  fuels,  compiled  from  analyses  and  experiments  by  the 
most  reliable  authors. 

TABLE  XI. 

Proportions  of  Ingredients  in,  and  Heat  G-enerated  by,  the 
Combustion  of  One  Pound  of  Fuel. 


Ingredients  in  One  Pound  of  Fuel. 

111 

Combustibles. 

Non-combustibles. 

Per  pound  of  fuel. 

Fuels. 

Car- 

Hydro- 

Sul. 

Nitro- 

Oxy- 

Ash. 

Air. 

Heat. 

Water 

rs? 

bon. 

gen. 

phur. 

gen. 

gen. 

evap. 

C' 

ir 

S' 

Jf 

a 

Cu.  ft. 

h. 

Ibs. 

1 

153 

14500 

124 

5  03 

1 

459 

62032 

53 

1  18 

Sulphur 

1 

114.4 

4032 

3.44 

182 

Peat  dry 

056 

006 

23 

0  15 

100 

99S4 

8.42 

74 

Woods  Oak 

048 

006 

041 

005 

784 

7580 

6  47 

967 

•'      White  Pine  

0.49 

0.08 



0.39 

0.04 

88.7 

8966 

7.65 

8.17 

«       Birch  

048 

0.07 

040 

0  05 

82.6 

8300 

707 

884 

Charcoal,  Oak  

0.88 

0.03 



0.06 

0.03 

144 

13760 

11.7 

5.34 

Pine  

0.72 

0.06 

0.04 

0.15 

0.03 

138.5 

12921 

11. 

5.67 

Maple  

0.70 

0.05 

0.05 

0.17 

0.03 

121 

13411 

11.45 

5.67 

Bituminous  Coal  

0.84 

0.05 

0.015 

0.012 

0.03 

0.05 

147 

14780 

12.62 

4.94 

Anthracite  Coal  

0.88 

0.01 

0.06 

135 

12760 

10.9 

5.73 

Coke  

0.8V 

0.02 

0.02 

0.008 

0.002 

0.06 

142 

13865 

11.85 

5.27 

1 

765 

4400 

3  76 

166 

CO  burning  to  CO2  

0.4286 



0.5714 

76.5 

10100 

8.63 

7.25 

Alcohol  

0.520 

0.137 

0343 

122  75 

12339 

10  55 

593 

Tallow 

079 

0  117 

0093 

169 

15550 

1327 

4.7 

Bees'  Wax,  White  

0.815 

0.139 

0.045 

186 

18900 

16.12 

3.88 

The  pounds  of  water  evaporated  per  pound  of  coal,  as  given  in  the 
table,  is  equal  to  the  units  of  heat  per  pound  of  steam,  of  pressure 
p  =  50  Ibs.  to  the  square  inch  above  that  of  the  atmosphere  =  1172.8 
units,  divided  into  the  units  of  heat  generated  by  the  combustion  of 
one  pound  of  coal. 

The  units  of  heat  per  pound  of  steam  of  any  pressure  is 

h  =  1082  +  0.305  T         ...        10 

This  is  the  heat  required  to  elevate  the  temperature  of  one  pound 
of  water  from  32°  Fahr.  to  boiling-point  and  evaporate  it  to  steam  of 
temperature  T.  See  table,  pages  400,  401,  Nystrom's  Pocket-Book. 


PROPERTIES  OF  FUEL.  51 


When  the  feed-water  is  of  higher  temperature,  a  reduction  is  re- 
quired as  follows  : 

w  =  pounds  of  water  heated  from  temperature  t  and  evaporated  to 
steam  of  temperature  T  per  pound  of  fuel  consumed. 

h'  =  units  of  heat  of  combustion  of  one  pound  of  coal  available  in 
evaporation. 


This  is  the  proper  formula  for  comparing  the  evaporative  quality 
of  different  fuels  consumed  in  similar  boilers  ;  and  when  similar  fuels 
are  used  in  different  kinds  of  boilers,  this  formula  gives  the  relative 
efficiency  of  the  boilers. 

Example.  Two  different  kinds  of  fuel  A  and  J5  are  experimented 
with  in  one  or  similar  boilers. 

One  pound  of  the  fuel  A  evaporates  w  =  7.5  Ibs.  of  water  from 
t  =  96°  to  steam  of  T=  297.84°. 

One  pound  of  the  fuel  B  evaporates  w  =  9  Ibs.  of  water  from 
€=115°  to  steam  of  !F=  31  1.86°. 

Required  the  available  units  of  heat  per  pound  of  each  fuel,  and 
their  relative  steaming  quality  ? 

A.  h'  =  7.5(1114  +  0.305  x  297.84°  -  96°)  =8203.3  units  of  heat. 

B.  h'  =  9(1114  +  0.305  x  311.86°  -  115°)  =  11917  units  of  heat. 


The  fuel  B  is  45  J  per  cent,  better  than  the  fuel  A. 

It  is  supposed  that  the  firing  and  draft  to  the  grate  and  other  cir- 
cumstances are  alike  in  both  experiments. 

Example  11.  Two  different  kinds  of  boilers  C  and  D  are  fired  with 
the  same  kind  of  fuel.  The  boiler  C  evaporates,  per  pound  of  coaJ 
consumed,  w  =  6  Ibs.  of  water  from  t  =  60°  to  steam  of  T=  393.94°. 

The  boiler  D  evaporates,  per  pound  of  fuel  consumed,  w  =  8  Ibs.  of 
water  from  t  =  85°  to  steam  of  T=  320.1°. 

Required  the  relative  qualities  of  the  two  boilers  ? 

C.  h'  =  6(1114  +  0.305  x  393.94°  -  60°)  =  7044.9  units  of  heat. 

D.  h'  =  8(1114  +  0.305x320.1°  -85°)  =9013.04  units  of  heat. 

D      Q01  3  04. 

Relative  quality  of  boilers,  ^  =  —    —  =  1.2794. 
C      /044.9 

The  boiler  D  is  nearly  28  per  cent,  better  than  the  boiler  C. 


52  STEAM  ENGINEERING. 


QUALITY    OF    BOILERS    AND    FUEL    COMPARED    WITH    A 
STANDARD    MEASURE. 

§  36.  The  most  simple  and  correct  way  of  comparing  the  quality  or 
economy  of  different  boilers  fired  with  the  same  kind  of  fuel,  or  of 
different  kinds  of  fuel  consumed  per  hour  in  the  same  kind  of  boilers, 
is  to  compare  the  units  of  heat  realized  by  evaporation  with  the  total 
units  of  heat  14500  due  to  the  combustion  of  one  pound  of  carbon  to 
carbonic  acid. 

In  the  preceding  four  examples  A,  B,  C  and  D  we  have  the  rela- 
tive economy  as  follows  : 


A  =  -  =  0.56575,  or  56  J  per  cent. 


_ 


14500 

_  0.4858,  or  48  1  per  cent. 

=  0.6216,  or  62  per  cent. 


14500 

Logarithm,  14500  =  4.1613680. 

The  fuel  B  gave  the  best  result,  and  the  boiler  C  the  poorest  ;  but 
the  question  now  arises  whether  or  how  much  of  the  economy  is  due 
to  the  fuel  or  to  the  boiler. 

The  percentage  of  carbon  in  a  fuel  ought  to  determine  its  quality, 
but  it  is  well  known  that  different  kinds  of  fuel  of  equal  proportions 
of  carbon  give  widely  different  results  in  the  evaporation  of  water  or 
generation  of  steam.  Theoretically,  the  percentages  given  in  the  last 
four  examples,  divided  by  the  percentage  of  carbon  in  the  respective 
fuels,  should  give  the  relative  quality  of  the  respective  steam-boilers. 

Suppose  the  fuel  used  in  the  boilers  C  and  D  to  contain  0.75  of 
carbon  ;  the  quality  of  these  boilers,  compared  with  the  natural  effect 
as  a  standard,  will  then  be 

C=—  =64.6  per  cent. 
0.75 

62 

D  -  —-  =  82.6  per  cent. 
0.75 

This  mode  of  comparing  the  quality  of  boilers  with  the  natural 
effect  as  a  standard  impresses  the  mind  at  once  with  merits  or 
economy  of  the  boilers. 


PETROLEUM  AS  FUEL. 


53 


EVAPORATION    FROM    212°. 

§  37.  The  comparison  of  steam-boiler  performance  with  the  evapora- 
tion of  water  from  and  at  212°  Fahr.  to  steam  under  atmospheric 
pressure  is  a  clumsy  standard  which  repeatedly  requires  explanation, 
and  even  then  is  not  always  well  understood.  There  have  been  many 
cases  in  which  boilermakers  maintained  that  the  horse-power  of  their 
boilers  should  be  calculated  by  the  evaporation  of  water  from  and  at 
212°,  while  water  cannot  be  pumped  into  the  boiler  at  tha£  tempera- 
ture. When  the  water  is  heated  between  the  feed-pump  and  the 
boiler,  it  is  done  so  at  the  expense  of  the  heat  generated  in  the  fur- 
nace or  by  the  exhaust  steam,  and  the  power  thus  gained  should  not 
be  credited  to  the  boilermaker. 

§38.    PETROLEUM    AS    FUEL. 


Substances. 

Pounds. 

Cu.  ft.  air. 

Units  of  heat. 

Carbon  

0.84 

126 

121SO 

Hydrogen  

0.16 

55 

9925 

1  00 

181 

22105 

One  volume  of  petroleum  requires  8400  volumes  of  air  for  complete 
combustion. 

One  gallon  of  petroleum  weighs  6.7  pounds. 

One  pound  of  petroleum  occupies  34.55  cubic  inches. 

One  cubic  foot  of  petroleum  weighs  50  pounds. 

Specific  gravity  of  petroleum,  0.8. 

One  barrel  of  petroleum  contains  about  42  gallons,  and  costs  in 
Philadelphia  about  six  dollars,  making  about  fifteen  cents  per  gallon. 

One  barrel  of  petroleum  weighs  about  282  pounds. 

Eight  barrels  of  petroleum  weigh  about  one  ton. 

One  ton  of  petroleum  costs  about  45  dollars. 

PERCENTAGE   OF   AVAILABLE    HEAT   OF   COMBUSTION. 

§  39.  When  the  percentage  of  carbon  in  a  fuel  is  known  (omitting 
hydrogen  and  sulphur),  we  can  determine  correctly  the  heat  generated 
per  pound  of  fuel  completely  consumed. 

C'  =  fraction  of  carbon  per  pound  of  fuel. 

The  heat  h  generated  per  pound  of  fuel  consumed  will  be 
h  =  14500  C",  the  gross  units  of  heat. 

h'  =  available  heat  generating  steam. 

Percentage  of  available  heat  =  —  ....         1 


54 


STEAM  ENGINEERING. 


Percentage  of  lost  heat  =  1 

Tihe  lost  heat  escapes  with  the  gases  of  combustion  through  the 
chimney.  The  available  heat  h'  is  found  by  Formula  11,  page  51. 

ECONOMY   OF   HEATING   THE   FEED-WATER. 

§  40.  The  following  Table  XII.  gives  the  percentage  of  gain  or  loss 
of  power  or  fuel  by  different  temperatures  of  feed-water  heated  or 
cooled.  The  first  column  contains  the  temperature  of  the  feed-water 
at  which  it  enters  the  boiler,  and  the  top  line  contains  the  temperature 
from  which  the  water  is  heated  or  cooled. 

Suppose  water  to  enter  the  feed-pump  at  32°  and  to  be  heated  to 
160°,  there  will  be  13  per  cent,  gained  in  power  and  fuel.  When 
water  enters  the  feed-pump  at  60°  and  is  heated  to  150°,  there  will  be 
10  per  cent,  gained. 

Suppose  the  water  in  the  heater  is  180°,  which,  when  passing  in  a 
long  pipe  to  the  steam-boiler,  is  reduced  to  150°,  the  loss  will  then  be 
3  per  cent.  The  signs  mean  +  for  gain  and  -  for  loss : 

TABLE  XII. 

Percentage  of  Power  or  Fuel  Gained  by  Heating  the 
Feed-water. 


Hi 

w^H 

32 

Temp 
40 

erature 
50 

from  v 
GO 

rhich  tl 
70 

ie  Feed  -water 
80        100 

s  Heated  01 
120     140 

Cool 
160 

»d. 
180 

200 

32 

0.0 

-1 

-1.5 

-2 

-3.4 

-4.4 

-6.5 

-9 

-11 

-13 

-iei-19 

40 

+  1 

0.0 

-0.5 

-1 

-2.4 

-3.4 

-5.5 

-8 

-10 

-12 

-15 

-18 

50 

+  1.5 

+  0.5 

0.0 

-0.5 

-2 

-3 

-4 

-7 

-9 

-11 

-14 

-17 

60 

+  2 

+  1 

+0.5 

0.0 

-1.4 

-2.4 

-3.5 

-6 

-8 

-10 

-14 

-16 

70 

+3.4 

+  2.4 

+  2 

+  1.4 

0.0 

-1 

-3 

-5 

fj 

-9 

-13 

-15 

80 

+4.4 

+  3.4 

+  3 

+  2.4 

+  1 

0.0 

-2 

-4 

-6 

-8 

-12 

-14 

90 

+  5.4 

+  4.4 

+  4 

+  3.4 

+  2 

+  1 

-1 

-3 

-5 

-7 

-11 

-13 

100 

+  6.5 

+  5.5 

+  5 

+  4.4 

+  3 

+  2 

0.0 

-2 

A 

-6 

-9.5 

-12 

110 

+  7.6 

+  6.6 

+  6 

+  5.6 

+  4.2 

+  3.2 

+  1 

-1 

-3 

-5 

-8 

-11 

120 

+  8.7 

+  7.7 

+  7 

+  6.7 

+  5.3 

+  4.3 

+  2.2 

0.0 

-2 

-4 

-7 

-10 

130 

+  9.8 

+  8.8 

+  8.3 

+  7.8 

+  6.4 

+  5.4 

+  3.3 

+  1 

-1 

-3 

-6 

-9 

140 

+  11 

+  10 

+  9 

+  9 

+  8 

+  7 

+4.5 

+  2 

0.0 

_2 

-5 

-8 

150 

+  12 

+  11 

+  10 

+  10 

+  9 

+  8 

+  5.5 

+  3 

+  1 

-1 

-3 

-7 

160 

+  13 

+  12 

+  11 

+  11 

+  10 

-t-9 

+  6.5 

+  4 

+  2 

0.0 

-2 

-6 

170 

+  15 

+  14 

+  12 

+  12 

+  12 

+  11 

+  8 

+  6 

+4 

+  2 

-1 

-4 

180 

+  16 

+  15 

+  14 

+  14 

+  13 

+  12 

+  9 

+  7 

+  5 

+  3 

0.0 

-3 

190 

+  17 

+  16 

+  15 

+  15 

+  14 

+  13 

+  10 

+  8 

+  6 

+  4 

-1 

-2 

200 

+  19 

+  1X 

+  17 

+  17 

+  16 

+  15 

+  12 

+  10 

+  8 

+  6 

-3 

0.0 

212 

+  20 

+  19 

+  18 

+  18 

+  17 

+  16 

+  14 

+  11 

+  9 

+  7 

-4 

+  1 

MANAGEMENT  OF  FIRE.  55 

MANAGEMENT    OF   FIRE    IN    STEAM-BOILERS. 

§  41.  When  the  air  enters  under  the  fire-grate  into  the  incandescent 
coal,  its  oxygen  unites  with  the  carbon  and  forms  carbonic  acid  gas 
C02,  which  rises  through  the  thick  layer  of  coal  and  absorbs  another 
atom  of  carbon,  forming  carbonic  acid  CO. 

This  carbonic  oxide  carries  with  it  small  particles  of  unconsumed 
carbon,  forming  smoke,  which  passes  through  the  flues  and  tubes,  and 
finally  through  the  chimney  into  the  air ;  the  result  of  which  is  an 
extravagant  waste  of  fuel. 

The  heat  generated  by  forming  carbonic  oxide  is  only  30  per  cent, 
of  that  generated  by  forming  carbonic  acid,  together  with  the  carry- 
ing off  of  unconsumed  carbon  in  form  of  smoke,  reduces  the  realized 
heat  to  a  very  small  percentage  of  that  due  to  the  complete  com- 
bustion of  the  fuel. " 

Therefore,  in  order  to  realize  the  greatest  economy  and  effect  of 
fuel,  it  must  be  consumed  to  carbonic  acid,  which  is  accomplished  by 
keeping  a  very  thin  and  even  layer  of  fire  on  the  grate,  and  by  having 
a  strong  draft.  For  anthracite  coal  the  thickness  of  the  fire  should 
be  between  4  and  6  inches,  and  for  bituminous  coal  from  6  to  8  inches. 
The  carbonic  acid  formed  will  then  rise  to  the  upper  surface  of  the 
fire  before  it  can  take  up  another  atom  of  carbon,  and  the  oxygen  in 
the  excess  of  air  not  utilized  in  the  fire  will  unite  with  the  uncon- 
sumed carbon  rising  above  the  coal,  and  form  the  flame. 

Anthracite  coal  forms  very  little  or  no  flame,  for  the  reason  that 
its  hardness  does  not  admit  of  faster  distillation  of  carbon  than  what 
is  immediately  consumed  by  the  oxygen  of  the  air  in  contact  there- 
with. 

Bituminous  coal  is  more  easily  volatilized,  and  the  bituminous 
matter  distills  faster  than  it  is  consumed  in  the  coal  fire.  The  oxygen 
of  the  air,  passing  through  the  incandescent  coal,  consumes  the  gaseous 
carbon  above  the  coal,  forming  a  flame  which  may  extend  some  ten 
feet  from  the  furnace  through  the  flues. 

The  area  of  entrance  for  air  through  the  coal  should  not  be  less 
than  one-fortieth  (^  of  the  area  of  the  fire-grate,  and  the  coal  layer 
should  be  of  even  thickness  and  cover  completely  the  whole  grate- 
surface,  so  that  no  air  can  enter  without  passing  through  or  between 
incandescent  coal.  Should  a  part  of  the  grate  be  uncovered  with 
coal,  a  body  of  air  will  enter  and  reduce  the  temperature  below  that 
of  ignition  in  that  part  of  the  furnace  bv  which  smoke  is  formed. 
Ashes  and  clinkers  in  the  grate  prevent  the  free  access  of  air,  and 
carbonic  oxide  and  smoke  are  formed.  An  experienced  fireman  can 


56 


STEAM   ENGINEERING. 


see  by  the  light  in  the  ash-pit  the  condition  of  the  fire  in  the  grate, 
and  he  slices  the  fire  accordingly.  When  the  furnace  is  charged,  the 
coal  should  be  spread  evenly  all  over  the  fire,  and  the  furnace  doors 
should  not  be  kept  open  longer  than  is  necessary  for  the  charge. 

PRODUCTS  OF  COMBUSTION. 

§  42.  The  term  "products  of  combustion"  should  mean  only  the 
binary  compound  of  oxygen  and  combustibles  formed  in  the  operation 
of  combustion,  such  as  carbonic  oxide,  carbonic  acid,  steam  and  sul- 
phurous acid  ;  but,  practically,  all  the  gases  in  the  furnace,  including 
nitrogen  and  smoke,  are  termed  products  of  combustion.  When 
hydrogen  is  consumed  in  the  furnace  and  forms  steam,  that  steam  is 
then  a  product  of  combustion ;  but  when  evaporated  from  moisture  in 
the  fuel,  it  is  not  a  product  of  combustion  in  the  furnace. 


TABLE  XIII. 
Properties  of  Products  of  Combustion. 


Gases  of  Combustion. 

Ato 
Symbol. 

mic 
Weight. 

Spe 
Gravity. 

Jiflc 
Volume. 

Weight  ar 
at 
Ibs.  per 
cu.  ft. 

d  volume 
>0°. 

cu.  ft. 
per  Ib. 

N20 
0 
N 
H 
C 
S 
CO 

cot 

HO 
H2O 
H& 

NO 

S02 

36 

8 
14 
1 
6 
16 
14 
22 
9 
8 
14 
22 
32 

1. 

1.104 
0.972 
0.0693 
0.8380 
1.123 
0.972 
1.527 
0.625 
0.555 
0.98 
1.525 
2.247 

1. 

0.9058 
1.0288 
14.430 
1.1933 
0.8904 
1.0288 
0.6549 
1.6 
1.8018 
1.0204 
0.6557 
0.4450 

0.0760 
0.0839 
0.0740 
0.000267 
0.06369 
0.0853 
0.0740 
0.11505 
0.0475 
0.04218 
0.07448 
0.1159 
0.19077 

13.158 
11.9189 
13.5135 
189.86 
15.701 
11.723 
13.5135 
8.6900 
21.0526 
23.7079 
13.4264 
8.6281 
5.2415 

Oxygen  

Nitrogen  

Carbon      

Carbonic  acid  
Steam 

Carburetted  hydrogen... 
Bicarbu  retted  hydrogen 
Nitrous  oxide  

GRATE-BARS. 

§  43.  The  proportion  of  thickness  of  grate-bars  to  the  air-space  be- 
tween them  varies  between  1  and  3  to  1,  depending  on  the  kind  of 
fuel  used  on  the  grate — that  is  to  say,  the  area  of  air-passage  between 
the  bars  varies  between  25  and  50  per  cent,  of  the  grate-surface. 


SMOKE-BURNING.  57 


The  following  table  gives  the  spaces  between  the  grate-bars  in  frac- 
tions of  an  inch,  as  generally  used  for  different  kinds  of  fuel. 

SPACE    BETWEEN    GRATE-BARS. 

Lehigh  anthracite  pea  coal ^  of  an  inch. 

Schuylkill     "          "       "   f      " 

Lehigh          "         chestnut  coal f      "  " 

Lehigh          "         stove         "    £      "  " 

Lehigh          "         broken     "    f      " 

Cumberland  bituminous  coal ^      "  " 

Ordinary  wood ^    to  1  " 

Sawdust j\  to  $  " 

SMOKE-BURNING. 

§  44.  The  burning  of  smoke  has,  since  the  time  of  Watt,  received  a 
great  deal  of  attention,  but  not  with  much  success,  owing,  first,  to  in- 
sufficient knowledge  of  the  chemistry  of  smoke,  which  in  Watt's  time 
was  not  sufficiently  developed  for  that  purpose ;  and  secondly,  the 
physical  properties  of  smoke  have  not  been  properly  considered  in  the 
attempt  to  burn  smoke. 

When  the  science  of  chemistry  was  sufficiently  advanced  to  enable 
us  to  determine  correctly  the  elements  of  combustion  and  of  smoke, 
we  have  still  not  fully  considered  the  physical  properties  bearing 
upon  the  success  in  smoke-burning. . 

It  is  well  known  that  smoke  consists  of  small  particles  of  carbon 
mixed  with  carbonic  oxide,  both  of  which  are  combustibles,  with  a 
sufficient  supply  of  oxygen  at  a  temperature  above  that  of  ignition 
between  700°  and  800°  Fahr.  It  appears,  therefore,  that  a  sufficient 
supply  of  air  among  the  smoke  in  the  furnace  would  accomplish  the 
object,  but  unfortunately  such  has  not  been  the  result. 

Suppose  a  case  of  one  pound  of  carbon  being  consumed  by  the  oxy- 
gen of  103  cubic  feet  of  air,  which,  according  to  Table  X.,  will  form 

Carbonic  oxide CO  =  1.5166  Ibs.  =   20.494  cubic  feet. 

Carbonic  acid C02  =  1.2833  Ibs.  =   11.126      " 

Nitrogen N    =6.2075  Ibs.  =   81.370     "       " 

Products  of  combustion      =  9.0074  Ibs.  =  112.990  cubic  feet. 

The  volume  is  here  taken  at  60°  Fahr. ;  but  at  a  temperature  above 
that  of  ignition,  say  800°,  the  volume  of  the  products  of  combustion 
will  be  2.5  x  1 13  =  282.5  cubic  feet.  (See  Law  of  Gases.) 

Of  this  volume  only  2.5x20.5  =  51.25  cubic  feet  is  combustible  or 


58  STEAM  ENGINEERING. 

carbonic  oxide,  which  requires  the  oxygeu  of  76.5x1.5166  =  115.9 
cubic  feet  of  air  at  60°  for  combustion  to  carbonic  acid. 

The  gases  of  combustion  are  not  chemically  combined,  but  me- 
chanically mixed  in  the  furnace,  and  arrange  themselves  into  layers 
according  to  their  specific  gravity,  the  lightest  occupying  the  top  and 
the  heaviest  the  bottom  of  the  furnace  or  flues.  The  specific  gravity 
of  nitrogen  and  carbonic  oxide  being  alike,  these  two  gases  will  mix ; 
but  the  nitrogen,  which  is  a  non-supporter  of  combustion,  occupies 
four  times  the  volume  of  that  of  the  combustible  carbonic  oxide. 

We  see  here  the  difficulty  of  uniting  the  oxygen  of  116  cubic  feet 
of  air  at  60°  with  2.5x11.126  =  37.8  cubic  feet  of  carbonic  oxide, 
which  is  already  mixed  with  2.5x81.37  =  203.42  cubic  feet  of  nitro- 
gen ;  therefore  the  burning  of  carbonic  oxide  to  carbonic  acid  by 
additional  supply  of  air  to  the  furnace  may  be  considered  very 
difficult,  if  not  impossible. 

When  the  carbonic  oxide  is  mixed  with  free  carbon  at  a  tempera- 
ture above  that  of  ignition,  the  oxygen  of  a  supply  of  air  is  easier 
united  with  these  combustibles,  but  even  then  the  large  quantity  of 
nitrogen  will  interfere  with  that  combustion. 

The  smoke  is  formed  first  when  the  temperature  of  the  products  of 
combustion  is  reduced  below  that  of  ignition,  before  which  time  the 
free  carbon  is  incandescent. 

In  most  of  the  attempts  made  to  burn  smoke  by  additional  supply 
of  air,  the  air  has  been  admitted  under  the  gases  of  combustion — that 
is,  from  behind  or  from  the  top  of  the  bridge,  where  it  first  comes  in 
contact  with  the  carbonic  acid,  and  perhaps  sulphuric  acid,  which 
prevents  the  air  from  being  mixed  with  the  combustibles  before  the 
temperature  is  reduced  below  that  of  ignition. 

The  admission  of  a  small  quantity  of  air  through  the  fire-door  or 
to  the  upper  part  of  the  furnace  has  proven  partly  successful  in  burn- 
ing some  smoke,  but  the  most  economical  combustion  of  the  fuel  is 
when  the  furnace  and  fire  are  so  arranged  that  the  fuel  is  completely 
consumed  by  the  air  entering  through  the  grate  into  the  fire. 


NATURAL   FURNACE-DRAFT. 

§  45.  The  natural  draft  to  a  furnace  is  caused  by  the  column  of 
heated  gases  in  the  chimney  being  lighter  than  an  equal  column  of  the 
surrounding  air.  The  weight  of  a  cubic  foot  of  dry  air  at  60°  is  532 
grains ;  and  suppose  the  hot  gases  in  the  chimney  to  weigh  286  grains 
per  cubic  foot,  then  a  chimney  of  one  square  foot  section,  and  say  50 
feet  high,  would  contain  50  cubic  feet,  and  the  weight  of  the  hot  gases 


DRAFT  IN  FURNACES.  59 

50x286  =  14300  grains.  The  weight  of  an  equal  column  of  air  at 
60°  would  weigh  50  x  532  =  26600  grains,  and  26600  -  14300  =  12300 
grains,  which  will  be  the  pressure  per  square  foot  of  the  draft. 

The  height  of  a  column  of  air  answering  to  this  pressure  is  12300  : 
532  =  23.12  feet.  The  velocity  of  the  draft  through  the  fire  (which 
is  the  smallest  aperture  of  entrance)  will  be  equal  to  that  a  body  would 
attain  by  falling  vertically  a  height  of  23.12  feet — namely,  36.44  feet 
per  second. 

The  combustion  of  one  pound  of  carbon  produces  by  153  cubic  feet 
of  air, 

Carbonic  acid  CO.,  =  3.6666  Ibs.  =    31.86  cubic  feet. 
Nitrogen  ^=8.9455  Ibs.  =  120.87      "       " 

Total    .    .    .    .  =12.6121  Ibs.  =  152.73      "       " 

We  see  here  that  the  volume  of  the  gases  of  combustion  is  nearly 
equal  to  that  of  the  air  supplied,  but  their  specific  gravity  is  slightly 
more— namely,  as  12.612  : 11.552  =  1.0918. 

Some  carbonic  oxide,  which  is  lighter  than  air,  always  accompanies 
the  gases,  for  which  we  may  with  safety  assume  the  sp.  gr.  of  the 
gases  of  combustion  to  be  equal  to  that  of  air  of  the  same  temperature. 
Therefore  the  sp.  gr.  of  the  hot  gases  in  the  chimney  will  be  equal  to 
the  reciprocal  of  the  volume  expansion  by  heat,  which  is  denoted  by  x 
in  the  Table  XXX.  for  law  of  gases. 

For  a  temperature  of  500°  of  the  gases  in  the  chimney  the  volume 
is  #  =  1.9491,  which  reciprocal  is  0.51308,  the  required  specific  grav- 
ity of  the  gases. 

The  height  of  the  chimney  is  to  the  height  of  a  column  of  cool  air 

of  equal  weight  to  that  of  the  hot  air  as  1  :  ( 1  —  I. 

V       *J 

A  =  section  area  of  the  chimney,  and 

B  =  area  of  the  fire-grate  in  square  feet. 

V=  velocity  of  the  air  through  the  fire. 

v  =  ascending  velocity  of  the  gases  in  the  chimney. 

H=  height  of  the  chimney  in  feet  above  the  fire-grate. 

The  area  for  passing  the  air  through  the  fire  should  be  about  one- 
fortieth  (^)  of  the  area  of  the  fire-grate. 

The  area  of  the  chimney  is  generally  made  about  0.16  of  the  area 
of  the  fire-grate. 

7=5 


60  STEAM  ENGINEERING. 

The  theoretical  coefficient  should  be  8  instead  of  5. 

BF 


Example  1.  The  height  of  a  chimney  is  H=  75  feet,  and  the  tem- 
perature of  the  ascending  gases  450°.  Required  the  velocity  of  the 
air  through  the  fire  ? 


Formula  1.         V-  5-J  75  (1 - — J- 29.38  feet  per  second. 

Example  2.  Required  the  velocity  of  the  ascending  gases  in  the 
chimney  when  B  =  3'6  square  feet  and  A  =  5.76  square  feet? 


Formula  2.  v  =  —    — 1/75  +  0.4588  =  4.58  feet  per  second. 

8x5.76 

It  is  assumed  in  these  examples  that  the  temperature  of  the  air 
is  32°,  but  for  other  temperatures  of  the  air  a  corresponding  reduc- 
tion should  be  made  of  the  temperature  of  the  hot  gases ;  for  exam- 
ple, when  the  air  is  75°  and  the  gases  450°,  then  75  -  32  =  43°,  and 
450-43  =  407°,  the  temperature  for  the  velocity  of  the  ascending 


The  factor  /I  —  J  in  the  Formulas  1  and  2  denoted  by  z  in  Table 
XXX.  is 


=(l--|- 
\      */ 


,  in  which, 


493+  T-t 


f=  temperature  of  the  ascending  gases  in  the  chimney,  and 
t  =  temperature  of  the  surrounding  air. 


As  in  Formula  1,  the  coefficient  5  in  Formula  4  should  be  8  by 
the  acceleration  of  gravity  V=  8\/gS;  but  the  friction  and  turning  of 
the  gases  amongst  the  incandescent  fuel  and  returning  tubes  reduce 
the  velocity  over  30  per  cent.,  for  which  reason  the  coefficient  is  re- 
duced from  8  to  5. 


WATER-GAUGE  FOR   CHIMNEY  DRAFT,  61 


WATER-GAUGE    FOR    CHIMNEY   DRAFT. 

§  46.  The  difference  of  pressure  between  the  hot  gases  in  the  chim- 
ney and  the  surrounding  atmosphere  is  very  small,  and  is  therefore 
measured  by  a  column  of  water. 

A  cubic  foot  of  water  at  32°  Fahr.  weighs  62.387  pounds,  whilst  a 
cubic  foot  of  air  of  the  same  temperature  weighs  only  0.0804186  of  a 
pound;  therefore  a  column  of  air  must  be  62.387  :  0.0804186  =  766.25 
times  higher  than  a  column  of  water  for  the  same  pressure. 

The  height  of  a  column  of  air  corresponding  to  the  difference  of 
pressure  in  and  outside  the  chimney  is 


x  =  volume  expansion  of  gases  by  heat  corresponding  to  the  tem- 
perature of  the  gases  in  the  chimney  from  the  Table  XXX. 
of  law  of  gases. 

77=  height  of  the  chimney  in  feet  above  grate. 
This  height  H',  divided  by  766.25,  gives  the  height  of  a  column  of 
water  of  equal  pressure,  and  multiplied  by  12  gives  the  height  in 
inches,  denoted  by  7. 


1    766.25V     x]    63.854V     */      '        '        2 


H(T-t) 


63.854(493+  T-t) 

The  following  Table  XIV.  is  calculated  from  this  formula  for  dif- 
ferent temperatures  T  of  the  gases  in  the  chimney,  and  that  of  the  air 
t  =  32,  and  for  different  heights  77  of  chimney. 

The  water-gauge  should  be  placed  as  near  the  level  of  the  fire-grate 
as  practicable. 


62 


STEAM  ENGINEERING. 


TABLE   XIV. 
"Water-gauge  in  Inches  for  Chimney-draft. 


Height  of 
Chimney. 

400 

Tern 
450 

leratnres  j 
500 

9  of  Oases  I 
550 

n  the  I  'iiin 
600 

ney. 
700 

800 

H. 

L 

/. 

/. 

1. 

/. 

L 

/. 

10 

0.0669 

0.0718 

0.0762 

0.0802 

0.0838 

0.0901 

0.0974 

15 

0.1000 

0.1077 

0.1143 

0.1203 

0.1257 

0.1356 

0.1430 

20 

0.1338 

0.1437 

0.1525 

0.1604 

0.1677 

0.1802 

0.1907 

30 

0.2008 

0.2155 

0.2287 

0.2407 

0.2515 

0.2703 

0.2861 

40 

0.2678 

0.2874 

0.3050 

0.3209 

0.3354 

0.3604 

0.3815 

50 

0.3346 

0.3592 

0.3812 

0.4011 

0.4192 

0.4505 

0.4768 

60 

0.4016 

0.4311 

0.4575 

0.4814 

0.5031 

0.5406 

0.5722 

70 

0.4685 

0.5029 

0.5337 

0.5616 

0.5870 

0.6307 

0.6676 

80 

0.5354 

0.5748 

0.6100 

0.6418 

0.6709 

0.7208 

0.7630 

90 

0.6024 

0.6466 

0.6862 

0.7221 

0.7547 

0.8109 

0.8584 

100 

0.6693 

0.7185 

0.7625 

0.8023 

0.8385 

0.9010 

0.9537 

125 

0.8366 

0.8981 

0.9531 

1.0028 

1.0481 

1.1262 

1.1921 

150 

1.0039 

1.0777 

1.1437 

1.2034 

1.2577 

1.3515 

1.4305 

175 

1.1712 

1.2573 

1.3343 

1.4039 

1.4673 

1.5767 

1.6689 

200 

1.3386 

1.4370 

1.5250 

1.6046 

1.6770 

1.8020 

1.9074 

250 

1.6732 

1.7962 

1.9062 

2.0057 

2.0962 

2.2525 

2.3842 

300 

2.0079 

2.1555 

2.2875 

2.4069 

2.5155 

2.7030 

2.8611 

400 

2.6772 

2.8740 

3.0500 

3.2092 

3.3540 

3.6040 

3.8148 

§47.  QUANTITY  OF  AIR  BY  NATURAL  DRAFT. 

Q  =•=  cubic  feet  of  air  passing  through  the  fire  per  hour  by  natural 
draft. 

£  =  90SF=450B 


The  average  quality  of  coal  may  be  assumed  to  contain  0.75  of  pure 
carbon,  and  153x0.75  =  115  cubic  feet  of  air  required  per  pound  of 
coal  consumed.  For  safety  say  140  cubic  feet. 

L  =  pounds  of  coal  consumed  per  hour  per  square  foot  of  grate. 

.    .        .        .        .        .        2 


L  =  : 


Example  8.  How  much  coal  will  be  consumed  per  hour  per  square 
foot  of  grate  by  a  chimney  of  H  =  60  feet  high,  the  temperature  of 
the  ascending  gases  being  500°  ? 


LOSS  OF  HEAT. 


Formula  3.    L  =  3.2^/60  (1 -  )  =  1 7.28  pounds. 

\      \         1.J49  I 

The  height  of  the  chimney  required  for  the  combustion  of  L  pounds 
of  coal  per  hour  per  square  foot  of  grate  will  be 

U 


10.29(14). 


LOSS  OF  HEAT  BY  THE  ESCAPING  GASES  OF  COMBUSTION. 

§  48.  The  heat  carried  off  by  the  gases  of  combustion  is  lost  for  the 
generation  of  steam,  but  utilized  for  creating  draft  to  the  furnace.  The 
higher  the  chimney  is,  the  more  will  that  heat  be  utilized  for  creating 
draft.  The  economy  consists  in  making  the  chimney  high  and  redu- 
cing the  temperature  of  the  ascending  gases  by  absorbing  more  of  the 
heat  for  evaporation. 

The  specified  heat  of  the  gases  of  combustion  averages  0.25.  See 
Specific  Heat.  The  weight  of  the  gases  per  pound  of  carbon  consumed 
to  carbonic  acid  is  12.612  pounds,  and  the  heat  carried  off  will  be 

A  =  12.612x0.25  (T-t)      ...        1 
A  =  3.153(T-t)         .         .      .  .        .        2 

e  =  fraction  of  carbon  per  pound  of  coal. 

L  =  pounds  of  coal  consumed  per  hour  per  square  foot  of  grate. 
A  =  units  of  heat  passing  through  the  chimney  per  hour. 


The  percentage  of  heat  lost  by  the  escaping  gases  will  then  be 

0.02175  (T-t)    ....        4 

Example  4-  The  temperature  of  the  ascending  gases  being  !F=  480°, 
and  that  of  the  surrounding  air  t  =  72°,  required  the  percentage  of 
heat  lost  through  the  chimney  ? 

0.02175(480  -  72)  =8.87  per  cent. 

It  is  supposed  in  this  example  that  all  the  carbon  is  perfectly  con- 
sumed to  carbonic  acid. 


64  STEAM  ENGINEERING. 


TEMPERATURE  OF  THE  GASES  IN  THE  CHIMNEY. 

§  49.  This  is  a  very  difficult  problem  to  solve  theoretically,  on  ac- 
count of  the  various  circumstances  involved  therein  making  a  very 
complicated  mathematical  demonstration,  the  result  of  which  would 
probably  not'  give  a  closer  result  than  does  the  following  formula, 
which  is  set  up  from  practice ;  namely, 


'=300^- 


B  +  a 

T = temperature  of  the  gases  when  entering  the  chimney. 

Example  1.  A  steam-boiler  of  B  =  96  square  feet  fire-grate  and 
_1  =  2880  square  feet  of  heating  surface  is  connected  with  a  chimney 
H=  47  feet  high.  Steam  pressure  p  =  62  pounds  to  the  square  inch. 
Required  the  temperature  of  the  gases  in  the  chimney  ? 


'-300^ 


-403.,  P., 


By  this  formula  we  can  find  the  temperature  in  any  part  of  the 
flues  or  tubes  by  subtracting  that  part  of  the  heating  surface  which 
the  fire  has  not  reached,  or  by  taking  the  heating  surface  exposed  to 
the  fire  up  to  the  point  where  the  temperature  is  required. 

Example.  Required  the  temperature  at  the  bridge  in  the  boiler  of 
the  preceding  example,  in  which  the  heating  surface  in  the  furnaces 
alone  is  Q  =  245  square  feet  ? 


It  is  assumed  in  this  formula  and  examples  that  the  cross-section 
of  the  chimney  is  A  =  0.16  B. 

The  temperature  in  the  chimney  ought  not  to  be  more  than  100° 
above  that  of  the  steam  in  the  boiler,  and  the  heating  surface  not 
more  than  a  =  36  B. 

The  proper  proportion  between  the  fire-grate  and  heating  surface 
depends  upon  the  steam-pressure,  or  rather  the  temperature  of  the 
steam  and  that  of  the  gases  in  the  chimney.  When  the  temperature 
of  the  latter  is  reduced  below  that  of  the  former,  heat  is  conducted 
from  the  water  back  into  the  flue,  which  operation  is  a  waste  of  fuel, 
material  and  labor  in  the  first  construction  of  such  boilers. 

In  locomotive  boilers  with  very  long  and  narrow  tubes  and  exhaust 
draft  in  the  chimney,  the  temperature  of  the  gases  has  often  been 


TEMPERATURE  IN  CHIMNEYS.  65 

reduced  below  that  of  the  water  and  steam  in  the  boiler,  the  result  of 
which  is  a  Avaste  of  fuel. 

In  marine  boilers  the  heating  surface  rarely  exceeds  36  B,  and  the 
temperature  of  the  gases  in  the  chimney  is  then  about  100°  over  that 
of  the  steam  in  the  boiler. 

Stationary  boilers  are  sometimes  made  with  heating  surface  =  50  H, 
and  the  temperature  of  the  gases  in  the  chimney  has  been  reduced 
below  that  of  the  steam  ;  but  the  water  evaporated  per  pound  of  com- 
bustibles has  been  less  than  with  smaller  proportions  of  heating 
surface. 

For  very  low  steam-pressure  the  heating  surface  may  advantage- 
ously be  made  =  50  B. 

When  there  is  no  heating  surface,  but  the  chimney  is  connected 
directly  to  the  fire-grate,  so  that  all  the  heat  ascends  in  the  chimney, 
the  temperature  will  then  be 


T=300l/7,/2T2.         ...        2 

Example  2.  Required  the  temperature  in  a  chimney  H  =  62  feet 
high,  connected  directly  with  the  fire-grate  without  water-heating  sur- 
face, but  that  all  the  heat  passes  up  the  chimney  ? 


T=  3001/7  ,/62  +  2  =  2244.5  Fahr. 

§50.  TEMPERING  OF  STEEL. 

The  temperature  of  the  gases  in  the  chimney  depends  much  upon 
the  construction  of  the  boiler  and  the  proportion  of  fire-grate  and 
heating  surface.  A  simple  way  of  measuring  this  temperature  ap- 
proximately is  by  inserting  a  polished  iron  wire  about  \  of  an  inch  in 
diameter ;  the  color  of  tempering  will  show  the  temperature,  corre- 
sponding with  the  following  table. 

The  property  of  heat  to  color  steel  or  iron  can  be  applied  for  ascer- 
taining the  temperature  in  flues  and  chimneys  of  steam-boilers,  and  for 
other  temperatures  limited  between  430°  and  600°  Fahr. 

Yellow,  very  faint,  for  lancets 430° 

"       pale  straw,  for  razors,  scalpels 450° 

"       full,  for  penknives  and  chisels  for  cast  iron....  470° 

Brown,  for  scissors  and  chisels  for  wrought  iron 490° 

Red,  for  carpenters'  tools  in  general 510° 

Purple,  for  fine  watch-springs  and  table-knives 530° 

Blue,  bright,  for  swords,  lock-springs 550° 

"     full,  for  daggers,  fine  saws,  needles 560° 

"     dark,  for  common  saws 600° 

5 


66  STEAM  ENGINEERING. 


EVAPORATION  OF  POUNDS  OF  WATER  PER  HOUR  PER  SQUARE 
FOOT  OF  HEATING  SURFACE. 

§  51.  The  evaporation  per  heating  surface  varies  directly  as  the  l.V 
power  of  the  difference  between  the  temperature  of  the  gases  of  com- 
bustion and  that  of  the  water  in  the  boiler.  The  temperature  of 
the  gases  is  determined  by  Formula  1,  paragraph  49,  and  the  tem- 
perature of  the  water  is  the  same  as  that  corresponding  to  the  steam- 
pressure.  The  evaporation  per  heating  surface  will  therefore  be  dif- 
ferent in  different  parts  of  the  boiler. 

h  =  units  of  heat  passed  through  each  square  foot  of  heating  sur- 

face per  hour. 
H=  units  of  heat  per  pound  of  steam  generated.    (See  Steam  Table, 

Nystrom's  Pocket-Book.) 
T=  temperature  of  the  gases  of  combustion  at  the  place  in  the 

boiler  where  the  rate  of  evaporation  is  calculated. 
t  =  temperature  of  the  water  or  steam. 

Ibs  =  pounds  of  water  evaporated  per  hour  per  square  foot  of  heating 
surface  at  the  place  where  the  temperature  of  the  gases  is  T. 

Units  of  heat,        7i  =  0.505  /(T-  t)3.  .         .         1 

„  0.505]/(T-t)3 

Evaporation,       Ibs.  =    -  -^.  .         .         2 

H 

Example  1.  The  temperature  in  a  boiler  furnace  is  T=1200\  and 
steam  pressure  80  pounds  to  the  square  inch,  which  corresponds  to 
t  =  324  temperature  of  the  steam.  Required  the  units  of  heat  passing 
through  each  square  foot  of  heating  surface  per  hour  ?  and  how  much 
water  will  be  evaporated  per  square  foot  of  heating  surface  per  hour  ? 

Units  of  heat,        h  =  0.505J/U200—  324J3  =  1  3093. 


Evaporation,      Ibs.  =  --  •  =  11  .09  pounds. 
1180.7 

Example  2.  In  the  same  steam-boiler  as  in  the  preceding  example, 
the  temperature  of  the  gases  entering  the  chimney  is  r=460°.  Re- 
quired the  evaporation  per  square  foot  of  heating  surface  at  the  end 
of  the  boiler  where  the  gases  of  combustion  enter  the  .chimney  ? 

Evaporation,        Ibs  =  °-50V  (46Q°  "  324)3  =  0.678  of  a  pound. 
1180.7 

The  rate  of  evaporation  can  thus  be  calculated  in  any  part  of  the 
boiler  by  first  calculating  the  temperature  T  from  Formula  1,  in 
paragraph  49. 


SAFETY-VALVES.  67 


FRESH    WATER    CONDENSERS. 

§  52.  Fresh  water  condensers  are  generally  made  of  brass  tubes 
about  |  of  an  inch  diameter  and  tinned  outside. 

h  =  units  of  heat  conducted  per  hour  through  each  square  foot  of 

tubes. 

!F  =  tempera  cure  of  the  steam  entering  the  condenser. 
t  =  temperature  of  the  water  entering  the  condenser. 
B  =  area  of  fire-grate  in  square  feet. 
Q  =  heating  surface  in  square  feet. 

A  =  tubular  area  in  square  feet  in  the  condenser,  required  to  con- 
dense the  steam  generated  by  the  boiler  B  Q. 


B  a.        ....         2 

Example  2,  How  much  tubular  condensing  surface  is  required  for 
a  boiler  of  B  =  128  square  feet  fire-grate,  and  heating  surface  LJ  =  3850 
square  feet  ? 

Condensing  surface,        A  =  3.5  j/  128x3850  =  2457  square  feet. 


SAFETY-VALVES. 

§  53.  The  area  of  a  safety-valve  should  be  sufficiently  large  to  let 
out  all  the  steam  the  boiler  can  generate  without  increasing  the  nor- 
mal working  pressure  of  the  boiler,  and  without  the  valve  lifting 
more  than  one-forty-eighth  (^)  of  its  diameter. 

A  =  area  in  square  inches  of  the  inner  circle  of  the  valvesit. 
a  =  area  through  which  the  steam  escapes,  which  is  equal  to  the 
circumference  of  the  inner  circle  of  the  valvesit  multiplied 
by  the  height  the  valve  is  lifted. 
p  =  steam-pressure  in  pounds  per   square  inch  above  that  of  the 

atmosphere. 
^j9  =  weight  in  a  fraction  of  a  pound  per  cubic  foot  of  the  steam  of 

pressure  p.     (See  Steam  Table,  Nystrom's  Pocket-Book.} 
^  =  steam-volume  compared  with  that  of  its  water  at  32°  Fahr. 
H  =  height  in  feet  of  a  column  of  steam  of  one  square  foot  section, 
which   weight  would   be  equal  to  the   steam-pressure  per 
square  foot,  or  1  44  p. 

F=  velocity  in  feet  per  second  of  the  steam  through  the  safety- 
valve. 


STEAM  ENGINEERING. 


The  weight  of  a  column  of  steam  of  height  H  and  weight  per  cubic 
foot  f  will  then  be  £Tf. 

That  is  to  say,        144^  =  5"^.       ...         1 

Height  of  column,      H=  lil?.      ...         2 


Velocity  of  steam,       F=  8  1/"B'=  96  J-2- 

v 


3 


=  cubic  feet  of  steam  discharged  through  the   safety-valve  per 
second. 

aV     8a     -_     96  a    J        2 


That  is  to  say,  the  steaming  capacity  of  the  boiler  in  cubic  feet  of 
steam  per  second  should  not  exceed 

Q- 

The  steaming  capacity  of  a  boiler  fired  with  a  given  kind  or  qual- 
ity of  fuel  depends  upon  the  area  of  the  fire-grate  and  heating  surface. 
With  natural  draft  the  average  evaporation  of  water  of  32°  to  Q  cubic 
feet  of  steam  per  second  in  ordinary  boilers  is 


9000 

This  should  be  equal  to  the  escape  of  steam  through  the  safety- 
valve,  Formula  5,  or 

"  3°Vy  "         9000 

From  this  formula  we  obtain  the  requisite  area  a  of  the  safety-valve 
for  letting  out  all  the  steam  the  boiler  can  generate — namely, 


Allowing  for  the  contraction  of  the  steam  through  the  valve, 

35  per  cent. 

For  guiding  wings  of  the  valve 20    "     " 

For  steam  generation,  Formula  6 20    "     " 

Reduction  for  safety 75    "      " 


SfT  OF  SAFETY-VALVES.  69 

Limiting  the  valve  to  lift  only  one-forty-eighth  of  its  diameter,  the 
coefficient  6000  in  Formula  8  will  be  reduced  to  288,  when  A  is  the 
area  of  the  inner  circle  of  the  valvesit. 


.     ...  9 

288      \f 

This  should  be  the  reliable  formula  for  the  requisite  area  of  the 
safety-valve  of  a  steam-boiler. 

Example  9.  —  A  steam  boiler  of  B  =  130  square  feet  of  fire-grate 
and  a  =  3372  square  feet  of  heating  surface,  carrying  p  =  49  pounds 
of  steam-pressure  per  square  inch  above  that  of  the  atmosphere.  Re- 
quired the  area  A  of  the  safety-valve  ? 

The  steam  volume  at  p  =  49  is  ^  =  403.29,  and  weight  per  cubic 
foot  of  steam  ^  =  0.15469  of  a  pound.  The  area  of  the  safety-valve 
will  then  be 


_  52.092  square  inches. 

The  Formula  9  can  be  reduced  to  a  very  simple  form  by  the  aid  of 
a  table,  for  which  make 

10 


SIT   OF   SAFETY-VALVES. 

§  54.  The  sit  of  a  safety-valve  should  be  flat,  and  not  conical.  A 
flat  joint  is  easier  ground  and  kept  tight  than  a  conical  one.  The 
width  of  a  valvesit  should  not  be  more  than  one-tenth  (-fa)  of  the 
cube  root  of  the  diameter  of  the  valve,  and  even  one-sixteenth  will 
answer  the  purpose. 

For  conical  valves  the  area  should  be 


A  = 


M  C08.V. 


v  =  angle  of  the  valvesit  to  the  plane  of  the  valve. 
For  an  angle  of  45°  cos.45°  =  0.707,  and, 


A_ 

0.707  M 


70  STEAM  ENGINEERING. 

The  columns  M  and  N,  in  the  following  Table  XV.,  are  calculated 
from  the  Formulas  10  and  11  for  different  steam-pressures  in  the  first 
column  p. 

The  formula  for  area  of  safety-valves  will  then  be  simply 


A 


Example  3.  —  Required  the  area  of  a  safety-valve  for  a  boiler  of 
B  =  36  square  feet  fire-grate,  and  a  =  1024  square  feet  heating  sur- 
face, to  carry  p  =  85  pounds  steam-pressure  ?  (See  Table  XV.) 


A  =  5—  =  9.375  square  inches. 

20.52 

If  the  same   boiler  should  be  limited  to  p  =  20  pounds  steam- 
pressure,  the  area  of  the  safety-valve  should  be, 

1/36  x  1024     , 

A  =  —  —  =  31.44  square  inches. 

6.107 

The  steam-volume  in  the  following  table  is  calculated  from  Fair- 
bairn's  formula. 


VELOCITY  OF  STEAM  FORCED  BY  ITS  PRESSURE  INTO  AIR  OR 
VACUUM. 

§  55.  The  velocity  of  steam  forced  by  its  pressure  into  the  atmo- 
sphere is 


When  the  steam  passes  into  a  vacuum,  the  velocity  will  be 


^P  =  weight  in  pounds  per  cubic  foot  of  steam. 

P  =  pressure  per  square  inch  above  vacuum. 

When  the  steam  passes  into  a  partial  vacuum  of  pressure^/ — that 
is,  the  difference  between  the  atmospheric  pressure  and  that  into 
which  the  steam  passes — the  velocity  will  be 

F-i 


SAFETY-  VAL  VES. 


71 


TABLE  XV. 

Area  of  Safety-valves  and  Velocity  of  Steam  Passing 

into  the  Air. 

Steam 
pres- 
sure. 

288   \p 

yVf- 

Vf= 

Velocity. 
96  N~ 

''airbairn's 
Steam 
volume. 

Weight  per 
cubic  foot 
of  steam. 

P- 

M. 

Logarithms. 

N. 

V. 

t- 

f 

5 

2.333 

0.3680283 

9.883 

948.77 

1219.7 

0.05119 

10 

3.675 

0.5652855 

12.56 

1205.7 

984.23 

0.06338 

15 

4.911 

0.6911552 

14.09 

1352.6 

826.32 

0.07550 

20 

6.107 

0.7858060 

15.12 

1451.5 

713.08 

0.08749 

25 

7.274 

O.S617983 

15.86 

1522.5 

627.91 

0.09936 

'  30 

8.427 

0.9256803 

16.43 

1577.3 

561.50 

0.11111 

35 

9.570 

0.9089105 

16.89 

1621.4 

508.29 

0.12273 

40 

10.70 

1.0292700 

17.26 

1656.9 

464.69 

0.13128 

45 

11.82 

1.0726430 

17.58 

1707.6 

428.42 

0.14566 

50 

13.21 

1.1208622 

17.85 

1713.6 

397.51 

0.15694 

55 

14.04 

1.1473753 

18.09 

1734.8 

371.07 

0.16812 

60 

15.14 

1.1800772 

18.30 

1756.8 

348.15 

0.17919 

65 

16.23 

1.2103496 

18.49 

1774.0 

328.06 

0.19015 

70 

17.32 

1.2385479 

18.66 

1791.3 

310.36 

0.20101 

75 

18.39 

1.2647646 

18.82 

1806.7 

294.61 

0.21185 

80 

19.46 

1.2891428 

18.97 

1821.1 

280.50 

0.22241 

85 

20.52 

1.3121774 

19.10 

1833.6. 

267.80 

0.23296 

90 

21.59 

1.3342526 

19.23 

1846.1 

256.31 

0.24340 

95 

22.66 

1.3552599 

19.35 

1857.6 

245.86 

0.25375 

100 

23.73 

1.3752764 

19.47 

1869.1 

236.31 

0.26400 

105 

24.78 

1.3941013 

19.57 

1878.7 

227.56 

0.27421 

110 

25.81 

1.4117624 

19.67 

1888.3 

219.50 

0.28422 

115 

26.85 

1.4289443 

19.76 

1897.0 

212.07 

0.29419 

120 

27.88 

1.4452367 

19.86 

1906.6 

205.18 

0.30406 

125 

28.91 

1.4610481 

19.95 

1915.2 

198.78 

0.31385 

130  29.95 

1.4763323 

20.05 

1924.8 

192.83 

0.32354 

135 

30.99 

1.4912226 

20.14 

1933.4 

187.26 

0.33315 

140 

32.11 

1.5066060 

20.24 

1943.0 

181.69 

0.34276 

72  STEAM  ENGINEERING. 

a  =  area  in  square  inches  through  which  the  steam  escapes. 

Q  =  cubic  feet  of  steam  passing  through  the  opening  a  per  second. 

m  =  coefficient  of  contraction  of  the  steam-jet,  which  varies  from 

0.64  to  1.     For  steam  escaping  through  valves  or  cocks  the 

coefficient  can  he  taken  to  m  —  0.75. 


144 
Placing  m  =  0.75,  we  have 


§  56.  When  steam  passes  into  air  of  atmospheric  pressure,  the 
velocity  and  cubic  feet  of  steam  discharged  per  second  are  easily  cal- 
culated by  the  aid  of  Table  XV.  —  namely, 

Velocity,  V=WN          .....        8 

Cubic  volume,  Q  =  Q.5aN      .        .        .        .    '     .         9 

Example  8.  Required  the  velocity  of  steam  passing  from  a  boiler 
and  under  p  =  65  pounds  pressure  ? 

V=  96  x  18.49  =  1775.04  feet  per  second. 

Example  9.  Required  the  volume  of  that  steam  passing  through  an 
orifice  of  a  =  1  .5  square  inches  ? 

Q  =  0.5  x  1.5  x  18.49  =  13.867  cubic  feet  per  second. 

Example  1.  Required  the  velocity  V  of  steam  of  pressure  p  =  65 
pounds  to  the  square  inch  above  that  of  the  atmosphere,  issuing  from 
the  boiler  into  the  air?  and  how  many  cubic  feet  will  be  discharged 
per  second  through  an  opening  a  =  0.75  of  a  square  inch  ?  When  the 
opening  is  through  a  thin  plate  in  which  the  steam-jet  is  contracted 
on  all  sides,  the  coefficient  is  m  =  0.64. 


Velocity,  V=  96     r-rr--  =  1775  feet  per  second. 

»  0.  1901o 

Steam  discharged,    Q  =  •  =  5.91  cubic  feet  per  second. 


DISCHARGE  OF  STEAM.  73 

Example  6.  What  quantity  of  steam  of  pressure  P=85  pounds  to 
the  square  inch  above  vacuum  will  pass  through  a  cock  of  a  =  0.45  of 
a  square  inch  into  a  vacuum  ? 


Q  =  0.5  x  QA5—f        =  4.627  cubic  feet. 

Example  S.  Steam  of  pressure  p  =  45  pounds  to  the  square  inch 
above  the  atmosphere  is  passing  into  a  partial  vacuum  of  18.33  inches 
mercury,  or  p'  =  9  pounds  to  the  square  inch.  Required  the  velocity 
of  the  steam?  and  how  much  will  pass  through  the  opening  of  a  =  1.25 
square  inches,  the  coefficient  of  contraction  being  m  =  0.8  ? 


7  feet  per  second. 

=  11.68  cubic  feet. 


,  144 

The  horse-power  per  volume  of  steam  consumed  per  hour  is  given 
by  Formula  1,  §  23,  in  which 

Q-Wty-1)    ....        10 

g     3600j>£      PQ 
13748.4      3.819 


P 
96mo    HT  2  fitT    3.819HP 


5.7285 


13 


This  formula  gives  the  horse-power  of  steam  of  pressure  p  escaping 
from  a  boiler  through  an  opening  a. 

Example  13.  What  horse-power  is  required  to  blow  a  steam-whistle 
4  inches  in  diameter,  when  the  opening  is  0.005  of  an  inch,  the 
steam-pressure  being  p  =  60  pounds  to  the  square  inch  above  atmo- 
spheric pressure? 

The  area  of  the  steam-whistle  is 

a  =  4  x  3.14  x  0.005  =  0.0628  of  a  square  inch. 


74  STEAM  ENGINEERING. 

In  this  case  the  steam  passes  through  a  taper  opening,  for  which  the 
coefficient  m  =  l. 

0.0628x60 


IP- 


5.7285 


This  seems  to  be  a  very  high  horse-power  for  a  steam-whistle,  but  it 
is  nevertheless  true  under  the  conditions  assumed. 


g  57.  HORSE-POWER  OF  STEAM-ENGINES   BY    VOLUME    OF   STEAM. 

(7=  cubic  feet  of  full  steam  used  in  each  single  stroke  in  the  steam- 

cylinder. 

n  =  double  strokes  of  piston  per  minute. 
p  =  steam-pressure  in  pounds  per  square  inch. 


3.819x60 

Example  1.  The  cubic  capacity  of  a  steam  cylinder  is  (7=6.5 
cubic  feet,  and  the  piston  makes  n  =  45  double  strokes  per  minute 
with  a  steam-pressure  of  p  =-  70  pounds  to  the  square  inch.  Required 
the  horse-power  of  the  engine  ? 

.     45  x  6.5  x  70 

.       IP  =  --  -  178.7  horse-power. 
114.O/ 

This  is  the  horse-power  of  the  high-pressure  engine  working  with 
full  steam. 

If  the  horse-power  of  the  same  engine  is  calculated  in  the  ordinary 
way,  it  will  be  180.7,  or  one  horse-power  more  than  in  the  example, 
which  is  the  power  consumed  by  the  force-pump  feeding  the  boiler 
with  water. 

When  the  steam  is  expanded  in  the  cylinder,  C  means  the  volume 
of  the  full  steam,  and  the  horse-power  of  the  full  steam  multiplied  by 
1+  hyp.  log.  of  the  expansion  is  the  horse-power  of  the  expanded 
steam. 

STEAM-PRESSURE   AND    REVOLUTIONS. 

§  58.  When  the  dimensions  of  the  boiler  and  engines  are  given,  to- 
find  the  relation  between  steam-pressure  and  revolutions  of  the 
engine. 

$•  =  steam-volume  compared  with  that  of  its  water  at  32°  for  the 
given  steam-pressure. 


STEAM-PRESSURE  AND  REVOLUTIONS.  75 

#  =  cubic  feet  of  unexpanded  steam  used  in  each  revolution  of  the 

engine  or  engines. 

n  =  number  of  revolutions  per  minute  of  the  engine. 
£  =  correction  for  temperature  of  feed-water,  Table  V. 
r  =  correction  for  height  of  chimney,  Table  VII. 

.  _     150  #n 


Rr 

TM 


150  n 


Example  1.  A  steam-engine  of  3  feet  diameter  of  cylinder  and  5  feet 
stroke  of  piston  is  to  make  n  =  70  revolutions  per  minute,  with  a 
boiler  of  B  =  164  square  feet  of  fire-grate  and  heating  surface  Q  =  4850 
square  feet.  The  steam  to  be  cut  oif  at  half  stroke;  feed-water  120°, 
for  which  5  =  1.087  ;  height  of  chimney  85  feet,  for  which  r  =  1.27. 
Required  what  steam-pressure  the  boiler  can  carry  under  the  above 
conditions  ? 

#=7.061  x5  =  35.305  cubic  feet  of  steam  for  each  revolution,  to 
which  add  for  clearance  and  steamport  1.7  cubic  feet,  making  #=37 
cubic  feet. 

150x37x70 
Steam  volume,        y —  =  274.94. 

1. 087  xl.27^/  164x4850  , 

Find  the  steam-pressure  corresponding  to  this  volume  (see  Steam 
Table,  Nystrom's  Pocket-Book),  which  is  82  pounds  to  the  square  inch, 
the  pressure  required. 

Example  2.  How  many  revolutions  per  minute  may  be  expected 
from  an  engine  using  #=15  cubic  feet  of  full  steam  of  50  pounds  to 
the  square  inch  for  each  revolution,  when  the  steam-boiler  is  B  =  84 
and  Q  =  2480  square  feet,  the  temperature  of  the  feed-water  being 
90°,  for  which  5  =  1.054,  height  of  chimney  40  feet,  for  which 
r  =  0.91? 


76  STEAM  ENGINEERING. 


The  steam-volume  for  50  Ibs.  is  ^  =  397.51. 

397.51  x  1.054  x  0.91i/84  x  2480     , 

Revolutions,       w  =  —  —  =  24.46. 

150x15 

Formula  4  gives  the  size  of  steam-boiler  required  for  a  given-sized 
engine  and  revolution  of  the  same. 

Example  4-  What  size  steam-boiler  is  required  for  an  engine  using 
%F=  20  cubic  feet  of  full  steam  of  pressure  60  pounds  to  the  square 
inch,  to  make  n  =  48  revolutions  per  minute ;  height  of  chimney  75 
feet  and  temperature  of  feed-water  100°  ? 


-'Sidjh^Li.l- 

Suppose  the  heating  surface  in  the  boiler  to  be  Q  =  25B,  then 
25  B2  =  86086.5. 

The  required  fire-grate,         B  -=  A/ '—  -=  58.68  square  feet. 

Heating  surface,  a  -  58.68  x  25  - 1 467  square  feet. 


§59.   QUANTITY  OF  FEED-WATER   BY  AREAS  OF  FIRE-GRATE  AND 
HEATING  SURFACE. 

W=  cubic  feet  of  water  to  be  fed  into"  the  boiler  per  minute. 
d  =  diameter  in  inches  of  the  pump-piston  or  feed-plunger. 
s  =  stroke  in  inches  of  piston  or  plunger. 
n  =  pumping  strokes  per  minute. 


150 


0.7854  <P  8  n  _-|/Ba 
~T728~~     =    150   ' 

d2  s  n  =  14.668|/BO. 

Add  36  per  cent,  for  feeding  the  boiler  with  safety  and  allowing  for 
slip-water. 

d2  *  n  =  20l/BT:F.     ....        2 


CAPACITY  OF  FEED-PUMP.  77 


4 


_ 
5 


Example  1.  How  much  water  is  required  per  minute  to  feed  a  boiler 
of  B  =  45  square  feet  fire-grate,  and  LJ  =  1250  square  feet  heating 
surface? 

1/45  x  1250  _       cub.c 
150 

Example  3. — What  diameter  must  be  given  to  a  feed-plunger  of 
s^S  inches  stroke,  making  n  =  50  strokes  per  minute,  to  feed  the 
boiler  of  B  =  36  square  feet  fire-grate  and  Q  - 1296  square  feet  heat- 
ing surface  ? 


=  \  / 

* 


2<V36xl296 
—  - 


oo-     u 
-  =  3.3  inches. 


§60.  CAPACITY   OF   THE   FEED-PUMP   BY   THE   SIZE   OF   THE 
STEAM-CYLINDER. 

D  =  diameter  in  inches  of  the  steam-cylinder,  double  acting. 

S  =part   of  the  stroke  in   inches   under   which   steam    is   fully 

admitted,  including  clearance  and  capacity  of  steamports. 
"^  =  Steam-volume  corresponding  to  the  steam-pressure. 
d  =  diameter  in  inches  of  the  pump-plunger,  single  acting. 
s   =  stroke  of  the  pump-plunger  in  inches. 

It  is  supposed  that  the  feed-pump  is  connected  with  the  engine,  so 
as  to  make  the  same  number  of  strokes  per  unit  of  time  as  does  the 
steam-piston. 

f  d*s  =  W2  S 


78  STEAM  ENGINEERING. 

Add  50  per  ceiit.  to  the  last  number  for  safety  in  feeding  the 
boiler  and  for  slip-water.  The  practical  formula  should  then  be 

Diameter  of  plunger  d  =  •*/  — —     .         .         .         1 

o  r\z  o 

Stroke  of  plunger  s  = .        .        .2 

Example  1. — The  diameter  of  a  steam-cylinder  is  D  =  36  inches, 
full  steam-pressure  75  pounds,  cut-off  at  32  inches,  to  which  add  for 
clearance  and  capacity  of  steam  ports  say  2  inches,  making  $  =  34 
inches.  The  stroke  of  the  feed-plunger  is  designed  to  be  s  =  24  inches. 
Required  the  diameter  of  the  plunger  ? 


13x36 
~  \  294.6: 


2~x~34 

=  1.8696  ;  say  2  inches. 


294.61  x  24 

RADIATION    OF   HEAT   FROM   STEAM-PIPES,  BOILERS   AND 
STEAM-CYLINDERS. 

§  61.  The  quantity  of  heat  radiated  from  a  hot  surface  into  the  air 
varies  directly  as  the  difference  of  temperature  of  the  hot  surface  and 
of  the  surrounding  air.  The  radiation  per  square  foot  is  not  constant 
for  cylindrical  surfaces  under  12  inches  in  diameter,  but  varies  in  an 
arithmetical  ratio  inversely  as  the  square  of  the  diameter — that  is, 
small  steam-pipes  radiate  more  heat  per  square  foot  of  surface  than 
do  large  ones  up  to  12  inches  diameter.  For  diameters  over  12 
inches  the  quantity  of  heat  radiated  is  directly  as  the  surface  exposed 
to  free  air. 

The  thickness  of  metal,  within  the  limit  of  ordinary  practice,  does 
not  seem  to  materially  affect  the  quantity  of  heat  radiated  from  un- 
covered surfaces. 

When  the  radiating  surface  is  covered  with  felt  and  canvas  outside, 
the  check  of  radiation  of  heat  is  greater  for  small  diameters  of  pipe 
than  for  larger  ones  with  the  same  thickness  of  covering,  as  will  be 
seen  in  the  accompanying  Table  XVI. 

D  =  outside  diameter  of  steam-pipe  in  inches. 

L  =  length  in  feet  of  cylinder  or  pipe. 

A  =  radiating  area  in  square  feet. 

f = temperature  Fahr.  of  the  steam  in  the  steam-pipe. 

t  -  temperature  of  the  external  air. 

h  =  units  of  heat  radiated  por  hour. 


RADIATION  FROM   UNCOVERED  SURFACES.  79 


(7=  cubic  feet  of  steam  of  temperature  T  condensed  per  hour. 

I  =  latent  heat  per  cubic  foot  of  steam  of  temperature  T,  which  is 

denoted  by  L'  in  Steam  Table,  see  Pocket-BooL 
p  =  pressure  per  square  inch  of  the  steam. 
IP  =  horse-power  lost  by  radiation. 
m  =  percentage  of  heat  or  power  gained  by  covering  the  pipe  with 

felt.     (See  Table  XVI.) 
n  =  exponent  of  the  wind,  which  varies  with  the  velocity  of  the 

current  of  air  passing  the  radiating  surface  as  follows : 

Calm.  Gentle.  Brisk.  Storm. 

w  =  1.2  n  =  1.22  n  =  1.24  w  =  1.26 


§62.  RADIATION    FROM    UNCOVERED   SURFACES. 
Heat  radiated  per  hour,        h  =  0.505^(  T-  t)n.      .         1 

For  cylinder  or  pipes  over  12  inches  in  diameter,  the  radiation  per 
fiour  will  be 

Units  of  heat,        A  =  0.1322Z>£(T- «)".         .         2 

For  cylinders  or  pipes  under  12  inches  in  diameter,  the  radiation 
per  hour  will  be 

Units  of  heat,      h=    DL    [450  +  (12-D)2](T- t)n.        3 
3404.8 

The  volume  in  cubic  feet  of  steam  condensed  per  hour  will  be 

*•! < 

Horse-power  lost  by  radiation  of  h  units  of  heat  per  hour  will  be 

5 

Example  1.  How  many  units  of  heat  are  radiated  per  hour  from  an 
uncovered  steam-boiler  exposing  A  =  198  square  feet  of  radiating  sur- 
face in  a  gentle  breeze  of  t  =  45°,  when  the  steam-pressure  in  the 
boiler  is  p  =  65  pounds  to  the  square  inch  ? 

Units  of  heat,        h  =  0.505  x  198(311.86  -  45)' •«  =  91206. 


80  STEAM  ENGINEERING. 

311.86-45  =  266.86. 

Logarithm,  266.86  =  2.4262835 

Multiply  by  exponent,  1.22 

48525670 
48525670 
24262835 


912.15  =  2.960065870 
Add  log.  198  =  2.2966652 

Add  log.  0.505  =  0.7032914  -  1 

Units  of  heat,    91206  =  49600225 

Example  4-   How  many  cubic  feet  of  steam  are  condensed  by  the 
radiation  of  h  =  91206  units  of  heat  per  hour  ?     Latent  heat,  I  =  170. 

91206  = 
170 

4.9600225 

Subtract  log.  170  =  2.2304489 

Cubic  feet  of  steam,  536.5  =  2.7295736 

Example  5.   How  much  horse-power  is  lost  by  the   radiation  in 
the  preceding  examples  ?     C  =  407.48  cubic  feet,  and  p  =  65  pounds 

Power  lost,          H>  =  53'5*65  =  2.5375  horse-power. 


log.      536.5  =  2.7295736  }  . 

log.  65  -1.8129134  )  ac 

4.5424870 

Subtract  log.  13748.4  =  4.1382521 

Horse-power  lost,        2.5375  =  0.4042349 

Example  2.  An  uncovered  steam-pipe  is  D  =  8  inches  diameter  and 
L  =  28  feet  long,  conducting  steam  of  p  =  80  pounds  pressure,  and 
temperature  T=324°.  The  temperature  of  the  surrounding  air  is 
£  =  40°  of  brisk  wind.  Required  the  units  of  heat  lost,  the  cubic  feet 
of  steam  condensed  per  hour  and  the  horse-power  lost  by  radiation 
from  the  pipe  ? 

O         00 

Units  of  heat,        h  =    -        [450  +  (1  2  -8)2]  (324  -4ff)lM  =  33780. 


COVERED  STEAM-PIPES.  81 

The  whole  calculation  is  practically  set  up  as  follows  by  log- 
arithms : 

Logarithm!. 
324-40  =  284  =  2.4533183 

Multiply  by  exponent, 1.24 

98132732 
'  49066366 

24533183 

(324  -  40)1-24  =  +  3.042114692 
(12  -  8)*  =  16  +  450  =  466  =  +  2.6683859 
8  x  28  =  224  =  +  2.3502480 
8  x  28[450  +  (12  -  8)2](324  -  40)1-24  =  +  8.0607486 

Coefficient, 3404.8  =  -  3.5320916 

The  required  units  of  heat,  .  .  h  =  33780  =  +  4.0286570 
Latent  heat  per  cubic  foot,  .  .  I  =  196.84  -  -  2.2943339 
Cubic  feet  of  steam  condensed,  .  C=  171.52  =  +  2.2343231 
Steam-pressure,  ....  p  =  80  =  +  1.9030900 

Cp=  +  4. 1374131 

Coefficient,  ....       13748.4-  -4.1382521 

Horse-power  lost,         .         .         IP  -  0.99807  =  +  0.9991610  - 1 
Say  one  horse-power  lost  by  radiation. 

It  is  supposed  in  this  example  that  the  steam  is  working  "a  high- 
pressure  engine  without  expansion.  For  a  condensing  engine  take 
the  steam-pressure  above  vacuum  and  multiply  the  lost  power  by 
1+hyp.Iog.  of  the  expansion,  and  the  product  will  be  the  correct 
horse-power  lost. 

COVERED    STEAM-PIPES. 

§  63.  When  the  steam-pipe  is  covered  with  felt  and  canvas  outside, 
there  is  very  little  heat  radiated,  as  will  be  seen  in  the  accompanying 
table,  which  gives  the  heat  and  power  saved  by  covering  of  different 
thickness. 

Suppose  the  loss  by  radiation  of  hoat  from  an  uncovered  steam-pipe 
6  inches  in  diameter  is  IP  =  2  horse-power ;  then,  by  covering  the 
pipe  with  felt  one  inch  thick  will  save  86  per  cent,  of  the  2  horse- 
power, or  2x0.86  =  1.72  horse-power,  and  the  loss  by  radiation  from 
the  covered  pipe  will  be  only  2  -  1.72  =  0.28  of  a  horse-power. 


82 


STEAM  ENGINEERING. 


TABLE  XVI. 

Percentage  w  of  Heat  or  Power  Gained  by  Covering  Steam- 
pipes  with  Felt  and  Canvas  Outside. 


Warn. 

j.U,e. 

T 

1       i 

hlekne 
i 

s  in  In 

1 

chex  o 
1 

r  Felt  < 
H 

Torerln 

2 

?• 

3 

4 

0 

D 

m     |    m 

m 

TO 

TO 

m 

m 

TO 

TO 

TO 

1 

65 

76 

81 

86 

92 

94 

96 

98 

99 

100 

2 

63 

74 

80 

85 

90 

93 

95 

97 

98 

99 

o 

61 

72 

79 

84 

89 

92 

95 

96 

98 

99 

4 

59 

71 

77 

83 

88 

92 

94 

96 

97 

99 

5 

57 

69 

76 

82 

87 

91 

94 

96 

97 

99 

6 

54 

67 

74 

81 

86 

91 

94 

95 

97 

99 

7 

r,-2 

66 

73 

81 

85 

90 

93 

95 

97 

99 

8 

50 

64 

71 

80 

85 

90 

93 

9-3 

97 

99 

9 

47 

62 

70 

79 

84 

89 

93 

95 

97 

99 

10 

45 

61 

69 

78 

84 

89 

92 

95 

98 

98 

11 

42 

59 

67 

78 

83 

88 

92 

94 

96 

98 

12 

40 

58 

66 

77 

83 

88 

92 

94 

96 

98 

STEAM-BOILER   EXPLOSIONS. 

§  64.  Steam-boiler  explosions  are  caused  by  suddenly  liberating  all 
the  work  stored  in  the  boiler. 

The  work  K  is  the  product  of  the  three  simple  physical  elements 
force  F,  velocity  V  and  time  T. 

W<yrk,K=FVT.  ...         1 

The  force  of  this  work  is,  therefore, 


When  the  steam-pressure  in  any  part  of  the  boiler  is  suddenly  re- 
moved by  bursting  of  the  shell,  the  entire  work  of  the  heat  stored  in 
the  steam  and  water  is  at  the  same  time  started  with  a  velocity  pro- 
portionate to  the  removed  pressure. 

When  the  pressure  is  suddenly  lowered  below  that  due  to  the 
temperature  of  the  water,  the  heat  in  it  generates  steam,  which  raises 
the  water  bodily  in  the  form  of  foam,  striking  the  steam-side  of  the 
boiler,  and  the  work  is  thus  suddenly  arrested.  If  the  time  of 
arresting  the  work  is  infinitely  small,  the  force  will,  according  to 
Formula  2,  be  infinitely  great,  and  thus  the  boiler  explodes. 


STEAM-BOILER  EXPLOSIONS. 


.  §  65.  Let  Fig.  3  represent  the  steam-boiler,  consisting  of  a  cylindri- 
cal tube  of  one  square  foot  section  and  of  indefinite  length.        Fig.  3. 
The  lower  end  of  the  tube  is  closed  and  contains  one  cubic 
foot  of  water,  from  which  steam  has  been  generated  by 
the  heat  of  the  lamp  L,  and  has  raised  the  piston  with 
the  weight  Q  a  space  S  from  the  surface  of  the  water. 

Assume  the  steam-pressure  to  be  P  =  65  pounds  to  the 
square  inch  above  vacuum,  and  one  cubic  foot  of  steam 
between  the  piston  and  the  water.  Then, 

In  one  cubic  foot  of  water,        H  =  15485  units  of  heat. 

In  one  cubic  foot  of  steam,       H'  =      184     "  " 

Total  heat  in  the  boiler,  H+H'  =  15669  units. 

Take  away  the  lamp,  so  that  no  more  heat  enters  into 
the  boiler. 

Diminish  gradually  the  weight  Q ;  the  expansion  of  the 
steam  will  then  raise  the  piston,  and  the  heat  in  the  water 
•will  evaporate  more  steam  until  the  temperature  corre- 
sponds with  the  reduced '  pressure.  The  temperature  of 
the  water  at  P=65  is  2*  =297.84°  ;  and  if  the  weight  Q 
is  gradually  reduced  to  14.7  pounds  to  the  square  inch  on 
the  piston,  the  temperature  of  the  steam  and  water  will 
be  212°  Fahr. 

One  cubic  foot  of  water  at  T=  287.84°  weighs  57.687  pounds,  of 
268.39  units  of  heat  per  pound. 

§  66.  At  the  temperature  212°  the  units  of  heat  per  pound  of 
water  are  180.9  and  per  pound  of  steam  1146.6.  The  question  now  is, 
How  many  pounds  of  water  w  and  how  many  pounds  of  steam  8  of 
temperature  212°  are  there  in  the  boiler? 

180.9  w+ 1146.6  «=  15485  units  of  heat. 

w  +  s  =  57.85  pounds. 
«»=>  57.69-*.    Then,  180.9  (57.69 -«)+ 1146.6  «- 15485. 

Complete  the  calculation,  which  will  give 

a  =5.228  pounds  of  steam  of  ...     5994.8  units  of  heat. 

w  =  52.46  pounds  of  water  of  ...     9490.0  " 

For  one  cubic  foot  of  steam  add     .     .      184  " 

Total 15658.8  " 

The  original  heat  was 15669.  " 

52.46  pounds  of  water  at  212°  =        .     0.8767  cubic  feet. 
5.228  pounds  of  steam  at  212°  =       .     135.58       " 
Add  one  cubic  foot  expanded  four  times      4 

Total  volume  of  steam  .          139.58 


84  STEAM  ENGINEERING. 


That  is  to  say,  the  piston  has  moved  139.58-1.12  =  138.46  fee.t 
from  the  position  occupied  when  the  weight  (J  \v;is  tir.-t  diminished. 
The  work  accomplished  by  this  operation  is  determined  as  follows  : 
5.228  pounds  of  steam  of  pressure  P=  65  =  35.7  cubic  feet. 
65  : 14.7  =  4.47  the  expansion  of  the  steam. 
Hyperbolic  log.  4.47  -  1.49734. 

Work  K=  144  x  65  x  35.7  x  1.4973  =  500330  foot-pounds. 
From  this  subtract  the  work  of  the  atmosphere,  which  is 
k  =  144  x  14.7  x  138.46  =  293100  foot-pounds. 
Then  500330  -  293100  =  207230  foot-pounds  of  work  done  against 

the  atmosphere. 

Divide  this  work  by  550  times  the  number  of  seconds  occupied  in 
its  execution,  and  the  quotient  will  be  the  horse-power  of  the  opera- 
tion. 

§  67.  Now  suppose  the  piston  to  be  firmly  fixed  in  the  position 
shown  by  the  illustration  Fig.  3,  and  instead  of  gradually  diminish- 
ing the  weight  Q,  let  it  be  suddenly  removed,  leaving  the  hole  o  open 
for  the  steam  to  escape.  The  moment  the  steam-pressure  on  the  sur- 
face of  the  water  is  removed  or  reduced,  the  heat  will  generate  steam 
of  a  pressure  of  65  pounds  to  the  square  inch  in  all  parts  of  the  water ; 
and  as  there  is  not  a  corresponding  pressure  on  its  surface,  the  steam 
will  lift  the  water  bodily  in  the  form  of  foam,  striking  the  immovable 
piston,  and  thus  explode  the  boiler. 

Under  the  conditions  assumed,  the  work  of  this  explosion  will  be 
911160  foot-pounds,  accomplished,  no  doubt,  within  the  time  of  one 
second,  in  which  case  207230  :  550  =  1337  horse-power  of  the  explo- 
sion of  only  oue  cubic  foot  of  water,  of  which  only  1  —  0.8767  =  0.1233 
of  that  cubic  foot  was  converted  into  steam. 

The  mystery  of  steam-boiler  explosions  is  thus  explained. 
§  68.  The  investigation  becomes  more  simple  by  way  of  algebraical 
formulas,  for  which  letters  will  denote — 

W=^  pounds  of  water  under  steam-pressure  in  the  boiler   before 

explosion. 

w  =  pounds  of  water  reduced  to  temperature  212°,  and  not  evap- 
orated in  the  explosion. 

Ibs.  =  pounds  of  water  evaporated  to  steam  in  the  explosion  and  ex- 
panded to  the  pressure  of  the  atmosphere. 

h  =  units  of  heat  per  pound  of  water  in  the  boiler  before  explo- 
sion. 

P  =  steam-pressure  in  pounds  per  square  inch  above  vacuum  in 
the  boiler  before  explosion. 


STEAM-BOILER  EXPLOSIONS.  85 

(7=  cubic  feet  of  steam  of  atmospheric  pressure  generated  by  the 
heat  iu  the  water  before  explosion. 

K=  destructive  work  of  the  explosion  in  foot-pounds. 

Units  of  heat  IF  A  =  181  w  +  1147  Ibs.     .        .  3 

dt<;=  JF-lbs.   .         .    '    .        .  4 

(JF-lbs.)  +  H471bs.      ...  5 


6 


The  weight  per  cubic  foot  of  steam  of  atmospheric  pressure  is  0.038, 
and  the  volume  of  steam  evaporated  and  expanded  in  the  explosion 
to  atmospheric  pressure  will  be  996  x  0.038  =  36.7. 


The  volume  of  this  steam  under  the  pressure  P  was 

14.7  C 
P-14.7 

The  gross  work  done  by  the  explosion  will  then  be 
144xl4.7PC,  P 

- 


From  this  work  should  be  subtracted  the  reaction  of  the  atmo- 
sphere, which  is  144x14.7  C. 

The  remainder   will   be  the   destructive  work   of  the   explosion, 

namely, 


Example  7.  —  A  steam-boiler  containing  125  cubic  feet  of  water 
explodes  under  a  steam-pressure  of  P=S5  pounds  to  the  square  inch. 
Required  the  destructive  work  of  the  explosion  ? 

.Under  this  pressure  the  temperature  of  the  water  is  316.08°,  and 
weighs  57.21  pounds  per  cubic  foot. 

W=  125  x  57.21  -  7151.25  pounds. 


86  STEAM  ENGINEERING. 

The  steam-volume  generated  by  the  explosion  is 

71  T!  9^5 

(7=  —      ^(287  -  181)  =  20655  cubic  feet. 
36.7 

K=  2116.8  x  2Q6o5/  _  85      hyp.log.-^-  -  1\  =  49200550  foot-pounds, 

the  required  work  of  destruction. 

This  work  is  equivalent  to  that  of  the  explosion  of  246  pounds  of 
gunpowder,  which  is  more  than  double  the  work  of  a  charge  from 
a  20-inch  gun.  A  great  part  of  the  work  of  steam-boiler  explosions 
is  consumed  in  setting  the  air  into  vibration,  which  makes  the  report. 

§  69.  A  laborer  working  8  hours  per  day  with  a  power  of  50  effect 
accomplishes  a  work  of  1,440,000  foot-pounds  of  work,  called  "  work- 
manday." 

The  work  of  the  above  steam-boiler  explosion  49200550  :  1440000  = 
34  workmandays.  It  would  require  34  men  to  work  one  day,  or  one 
man  34  days,  to  do  the  same  amount  of  work. 

The  work  of  the  steam  in  the  boiler  prior  to  the  explosion  is  not 
included  in  the  preceding  formulas  and  examples,  because  it  is  an 
insignificant  quantity  compared  with  that  of  the  heat  in  the  water. 
The  bursting  of  a  vessel  full  of  steam  without  water  will  cause  very 
little  damage  compared  with  that  of  a  vessel  full  of  water  under 
steam-pressure. 

c  =  cubic  feet  of  steam  in  a  boiler  of 
P=  pressure  per  square  inch  above  vacuum. 
k  =  work  of  explosion  of  the  steam  only. 


CAUSE   AND   PREVENTION   OF   STEAM-BOILER    EXPLOSIONS. 

§  70.  The  bursting  of  a  steam-boiler  is  a  preliminary  process  to  the 
explosion. 

In  a  vessel  composed  of  any  non-elastic  material  and  filled  with 
water  hermetically  sealed  in  it,  if  that  water  is  frozen  solid,  the  ex- 
pansion of  the  ice  will  most  likely  burst  the  vessel,  but  there  will  be 
no  explosion,  because  there  is  no  explosive  agency  in  it. 

A  steam-boiler  full  of  cold  water  and  tested  with  hydrostatic  pres- 
sure until  it  bursts,  will  not  explode  ;  but  if  that  cold  water  is  heated 
to  a  temperature  corresponding  to  the  bursting  pressure,  there  will  be 
an  explosion. 


CAUSE  OF  BOILER  EXPLOSIONS.  87 

The  iron  in  steam-boilers,  like  any  other  material  subjected  to 
bursting  strain,  breaks  at  the  weakest  point ;  but  it  is  difficult  to  find 
the  location  of  that  point,  and  very  often  boilers  are  not  constructed, 
inspected  or  managed  with  sufficient  care  to  guard  against  bursting. 
Thus  steam-boiler  explosions  are  caused  by  various  neglects  in  guard- 
ing against  such  accidents — namely, 

First.  By  long  use  boilers  become  weakened  by  corrosion,  which  acts 
unevenly  on  different  kinds  of  iron  and  in  different  parts  of  the  boiler, 
and  if  not  properly  inspected  and  the  weakened  places  repaired,  the 
boiler  may  burst  and  explode. 

Second.  The  general  construction,  with  staying  and  bracing  of 
steam-boilers,  is  often  very  carelessly  executed,  and  results  in  explo- 
sion. This  kind  of  explosions  are  often  indicated  long  before  the  acci- 
dent occurs,  by  leakage  of  the  boiler;  when  the  engineer,  not  suspect- 
ing the  approaching  danger,  limits  the  remedies  generally  to  efforts 
toward  stopping  the  leak.  Leakage  from  bad  caulking  or  packing  Is 
easily  distinguished  from  that  of  bad  or  insufficient  bracing,  in  which 
latter  case  the  fire-  ought  to  be  hauled  out,  the  steam  blown  off  grad- 
ually, and  the  boiler  secured  with  proper  bracing. 

Third.  The  strength  and  quality  of  iron  in  the  original  construction 
are  not  always  properly  selected  to  correspond  with  the  duty  expected 
of  the  boiler,  which  neglect  causes  explosion. 

Fourth.  Single-riveted  joints  weaken  the  strength  of  a  boiler  abou* 
50  per  cent,  of  that  of  the  solid  plate,  and  boilers  therefore  often  burst 
by  tearing  the  plate  between  the  rivets.  This  defect  can  be  remedied 
by  making  double-riveted  joints,  which,  if  properly  proportioned,  are 
(by  experiments)  as  strong  as  the  solid  plate. 

Fifth.  Explosion  is  sometimes  caused  from  low  water  in  the  boiler, 
but  more  rarely  than  is  generally  supposed.  When  the  fire  crown  and 
flues  are  subjected  to  a  strong  heat  and  not  covered  with  water,  the 
steam  does  not  absorb  the  heat  fast  enough  to  prevent  the  iron  from 
becoming  so  hot  that  it  cannot  withstand  the  pressure,  but  collapses 
from  weakness,  and  the  boiler  explodes.  There  are  several  good  inven- 
tions for  preventing  too  low  water  in  boilers,  which  should  invariably 
be  used. 

Sixth.  Steam-boilers  often  burst  from  strain  in  uneven  expansion  or 
shrinkage  of  the  iron  by  sudden  change  of  temperature.  When  the 
fire  is  too  quickly  lighted  or  extinguished,  there  is  not  time  enough  for 
the  heat  to  communicate  alike  to  and  from  all  parts  of  the  boiler,  the 
effect  of  which  has  often  been  the  cause  of  bursting  the  boiler.  When 
cold  feed-water  is  injected  near  to  the  fire-place,  it  absorbs  the  heat 
quickly  and  cools  that  part  of  the  heating  surface,  and  when  the  feed 


88  STEAM  ENGINEERING. 

is  not  evenly  supplied,  but  alternately  stopped  and  forced  in  with  the 
full  capacity  of  the  pump,  there  will  be  a  corresponding  contraction 
and  expansion  of  that  part  of  the  iron,  the  work  of  which  is  injurious 
to  and  may  finally  cause  the  bursting  of  the  boiler.  The  feed-water 
should  be  heated  to  at  least  100°  for  condensing  engines  and  180° 
for  high-pressure  engines,  and  injected  at  some  distance  from  the  fur- 
nace. 

Seventh.  It  is  a  very  bad  practice  to  make  boiler-ends  of  cast-iron, 
composed  of  a  flat  disc  of  from  two  to  three  inches  thick,  with  a  flange 
of  from  one  to  two  inches  thick,  with  cast  rivet  holes.  The  first 
shrinkage  in  the  cooling  of  such  a  plate  causes  a  great  strain,  which 
is  increased  by  riveting  the  boiler  to  it.  Any  sudden  change  of  tem- 
perature in  such  plate,  either  by  starting  or  putting  out  the  fire,  might 
crack  the  plate  and  cause  explosion  of  the  boiler. 

Such  accidents  can  be  avoided  by  making  the  boiler-ends  of 
wrought-iron  plates  properly  stayed  or  made  concave  on  the  steam 
side. 

Eight.  In  cold  weather,  when  the  boilers  have  been  at  rest  for  some 
time,  the  water  in  them  may  be  frozen  to  ice  ;  then,  when  fire  is 
quickly  made  in  them,  some  parts  are  suddenly  heated  and  expand, 
whilst  other  parts  still  remain  cold,  thus  causing  an  undue  strain 
which  may  so  injure  the  boiler  that  it  will  not  be  able  to  bear  the 
required  steam-pressure,  and  explosion  follows. 

Such  accident  can  be  avoided  by  a  slow  and  cautious  firing,  so  that 
all  the  ice  may  be  thoroughly  melted  before  steam  is  generated  in  any 
part  of  the  boiler. 

Ninth.  When  a  number  of  boilers  are  placed  close  together  and 
connected  to  a  common  steam-pipe,  the  weakest  part  in  either  one  of 
them  is  the  measure  of  safety  for  all  the  rest ;  for  however  strong  the 
other  boilers  may  be,  when  the  weakest  one  bursts  all  the  rest  will 
most  likely  explode  simultaneously,  as  has  often  been  the  case. 

Tenth.  Steam-boiler  explosions  are  thus  not  always  caused  by  the 
pressure  of  steam  alone,  but  most  frequently  by  the  expansion  and 
contraction  of  the  iron  composing  the  boilers.  A  steam-boiler  which 
is  perfectly  safe  with  a  working  pressure  of  200  pounds  may  explode 
with  a  pressure- of  20  pounds  to  the  square  inch. 

Eleventh.  See  "  Superheating  Steam  "  for  another  possible  cause  of 
expk 


STRENGTH  OF  BOILERS.  89 

STRENGTH   AND    SAFETY    OF    STEAM- 
BOILERS. 

§  71.  The  law  in  the  United  States  regulating  the  strength  and 
safety  of  steam-boilers,  passed  by  Congress  February  28,  1871,  and 
enforced  February  28, 1872,  is  that  all  the  plates  used  in  steam-boilers 
shall  be  stamped  with  the  number  of  pounds  equal  to  the  break- 
ing-strength per  square  inch  section  of  the  iron.  One-sixth  of  the 
stamped  number  is  taken  as  the  safety  or  working  strength  of  the  iron 
in  the  boiler. 

The  law  requires  that  steam-boilers  must  be  tested  with  hydrostatic 
pressure  of  50  per  cent,  above  the  working  pressure  allowed. 

The  following  quotations  are  copied  from  the  rules  prescribed  for 
the  Boiler  Inspectors : 

"  Where  flat  surfaces  exist,  the  inspector  must  satisfy  himself  that 
the  bracing,  and  all  other  parts  of  the  boiler,  are  of  equal  strength 
with  the  shell,  and  he  must  also,  after  applying  the  hydrostatic  test, 
thoroughly  examine  every- part  of  the  boiler  to  see  that  no  weakness 
or  fracture  has  been  caused  thereby.  Inspectors  must  see  that  the 
flues  are  of  proper  thickness  to  avoid  the  danger  of  collapse.  Flues 
of  sixteen  inches  in  diameter  must  not  be  less  than  one-quarter  of  an 
inch  in  thickness,  and  in  proportion  for  flues  of  a  greater  or  less 
diameter." 

"  Every  iron  or  steel  plate  intended  for  the  construction  of  boilers 
to  be  used  on  steam-vessels  shall  be  stamped  by  the  manufacturer  in 
the  following  manner,  viz. :  At  the  diagonal  corners,  at  a  distance  of 
about  four  inches  from  the  edges,  and  also  at  or  near  the  centre  of  the 
plate,  with  the  name  of  the  manufacturer,  the  place  where  manufac- 
tured, and  the  number  of  pounds  tensile  strain  it  will  bear  to  the  sec- 
tional square  inch." 

"  The  manner  of  inspecting,  testing  and  stamping  boiler-plates,  by 
the  United  States  inspectors,  shall  be  as  follows,  viz. : 

"  The  sheets  to  be  inspected  and  tested  shall  be  selected  by  the  in- 
spectors, indiscriminately,  from  the  lot  presented,  and  shall  not  be 
less  than  one-tenth  of  the  entire  lot  so  presented,  and  from  every  such 
selected  sheet  the  inspector  shall  cause  a  piece  to  be  taken,  for  the 
purpose  of  ascertaining  its  strength,  the  area  of  which  shall  equal  oiie- 
quarter  of  one  square  inch,  and  the  force  at  which  this  piece  can  be 
parted  in  the  direction  of  its  fibre  or  grain,  represented  by  pounds 
avoirdupois  multiplied  by  four,  shall  be  the  tensile  strength,  and  the 
lot  from  which  the  test-sheets  were  taken  shall  not  be  marked  above 


90  STEAM  ENGINEERING. 


the  lowest  number  represented  by  these  tests.  The  inspector  shall 
also  subject  a  piece  taken  from  each  selected  sheet  to  repeated  heating 
and  cooling,  and  shall  bend  it  short,  both  in  a  hot  and  a  cold  state, 
and  shall  draw  it  out  under  the  hammer,  as  it  is  called,  in  order  to 
ascertain  the  other  qualities  mentioned  in  Section  36  of  the  act  afore- 
said ;  and  should  these  test-pieces  be  found  deficient  in  these  qualities, 
the  inspectors  shall  refuse  to  place  the  government  stamp  on  the  lot 
from  which  these  test-sheets  were  taken ;  but  if  the  test-pieces  should 
prove  to  possess  these  qualities,  then  the  inspector  shall  proceed  to 
stamp  the  entire  lot  from  which  they  were  taken  with  the  letters 
'U.S.'  and  the  figure  denoting  the  inspection-district  in  which  the 
inspection  was  made." 

"  All  boiler-plates  tested  and  stamped  as  above  shall  be  considered 
as  having  been  inspected  according  to  law ;  but  should  any  local  or 
other  inspector  have  valid  reasons  for  believing  that  fraud  has  been 
practiced,  and  that  the  stamps  upon  any  such  boiler-plates  are  false, 
in  whole  or  in  part,  he  is  empowered  to  re-inspect  and  test  the 
same." 

"  The  provisions  of  this  rule  shall  take  effect  as  soon  as  the  inspec- 
tors are  appointed,  and  the  manufacturers  of  boiler-plates  notified  of 
the  same." 

The  rule  for  proportioning  the  strength  of  boilers  to  the  steam-pres- 
sure is  as  follows : 

Rule.  "  Multiply  one-sixth  (  £  )  of  the  lowest  tensile  strength  found 
stamped  on  any  plate  in  the  cylindrical  shell  by  the  thickness  ex- 
pressed in  parts  of  an  inch  of  the  thinnest  plate  in  the  same  cylindrical 
shell,  and  divide  the  product  by  the  radius  or  half  the  diameter  of  the 
shell  expressed  in  inches,  and  the  quotient  will  be  the  steam-pressure 
in  pounds  per  square  inch  allowable  in  single-riveted  boilers,  to  which 
add  twenty  per  centum  for  double  riveting." 

No  allowance  is  made  by  this  rule  for  the  metal  punched  away  by 
the  holes  in  the  plate.  Allowing  66  per  cent,  of  metal  between  the 
holes,  the  safety  strength  will  be  one-quarter  of  the  ultimate  strength. 

The  rule  is  more  simply  expressed  by  algeb'raical  formulas,  as 
follows : 

S  =  breaking-strain   in  pounds  per  square   inch,  stamped  on  the 

boiler-plate. 

t  =  thickness  of  the  plate  in  fractions  of  an  inch. 
D  =  inside  diameter  of  the  boiler  in  inches. 

p  =  steam-pressure  in  pounds   per  square   inch   allowable  in  the 
boiler,  single  riveted. 


STRENGTH   OF  RIVETED  JOINTS.  91 


\  72.  Safety  Strength  of  Single-Riveted  Joints. 

Si 

feteam-pressure,  p  = .       .         .         .         .         .1 


Diameter  of  boiler,      D  <=  — . 
3p 

q     T\ 

Thickness  of  plate,         t  =  — 

S 


Breaking-strain,  >S 

i 

Example  1.  A  steam-boiler  of  D  =  48  inches  diameter  and  thick- 
ness of  plates  i  =  0.375  of  an  inch  is  stamped  with  a  breaking-strain 
S  =  55,000  pounds.  Required  the  steam-pressure  the  boiler  is  allowed 
to  carry  ? 

55000  x  0.375 
p  = —  =  143.2  pounds  to  the  square 

inch  for  single-riveted  joints. 

For  double-riveted  joints  143.2x1.2  =  171.8  pounds  to  the  square 
inbh. 

i  73.  Safety  Strength  of  Double-riveted  Joints. 

C\A   S  f 

.    5 


Steam-pressure, 

P         D 

Diameter  of  boiler, 

D     QASt 

P 

Thickness  of  plate, 

i-.2t 

0.4  S 

Breaking-strain, 

S=D?, 
0.4* 

Example  8.  A  double-riveted  boiler  is  to  be  constructed  to  carry 
p  =  80  pounds  of  steam  in  a  diameter  D  =  96  inches,  with  t  =  0.3  of 
an  inch  thickness  of  plate.  Required  the  stamp  on  the  plates  ? 

£  =  _96^80  _  64000st 
0.4  x  0.3 

The  following  tables  are  calculated  from  the  above  formulas  for  .sin- 
gle and  double-riveted  boilers. 


92 


STRENGTH    OF    STEAM-BOILERS. 


TABLE  XVII. 

Boiler  Plates  Stamped  45.OOO  Ibs.  Safety-strain  £  =  75OO. 

•s| 

Thickness  of  boiler-plate  in  fractions  of  an  inrh. 

SJ 

&=  0.1875 

}  =  0.25 

&  =  0.28125 

&  =  0.3125 

ft  =  0.34375 

I* 

Riveting. 

Riveting. 

Riveting. 

Riveting. 

Riveting. 

y 

Single.  J  Double. 

Single. 

Double. 

Single. 

Double. 

Single. 

Double. 

Single. 

Double. 

D 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

36 

78.12 

93.74 

104.2 

125. 

117.2 

140.6 

130.2 

156.2 

143.2 

171.8 

38 

74. 

88.8 

98.6 

118.3 

110.9 

.133.1 

123.3 

148. 

135.6 

162.8 

40 

70.31 

84.37 

93.7 

112.4 

105.4 

126.5 

117.2 

140.6 

128.1 

154.7 

42 

66.96 

80.35 

89.2 

107. 

100.4 

120.5 

111.6 

133.9 

122.7 

147.3 

44 

63.92 

86.7 

85.2 

102.2 

95.85 

115. 

106.5 

127.8 

117.1 

140.5 

48 

58.59 

70.3 

78.1 

93.72 

82.87 

99.45 

97.65 

117.2 

107.4 

128.9 

54 

52. 

62.4 

69.44 

83.32 

78.12 

93.74 

86.S 

104.2 

95.5 

114.6 

60 

46.87 

56.24 

62.5 

75. 

70.31 

84.37 

78.12 

93.74 

85.93 

103.1 

66 

42.79 

51.34 

56.86 

68.17 

63.93 

76.71 

71. 

85.2 

78.1 

93.72 

72 

39. 

46.8 

52. 

62.4 

58.55 

70.26 

65.1 

78.12 

71.61 

85.93 

78 

36. 

43. 

49.34 

58.86 

54.67 

65.6 

60. 

72.1 

66.05 

79.26 

84 

33.48 

40.17 

44.64 

53.56 

50.22 

60.26 

55.8 

66.96 

61.38 

73.65 

90 

31.25 

37.5 

41.66 

50. 

46.83 

56.19 

52. 

62.5 

57.25 

68.7, 

96 

29.28 

35.53 

39. 

46.8 

43.91 

52.69 

48.82 

58.58 

53.7 

64.44 

102 

27.56 

33.07 

36.76 

44.11 

41.35 

49.62 

45.95 

55.14 

50.53 

60.64 

108 

26. 

31.2 

34.72 

41.86 

39.06 

46.87 

43.4 

52.1 

47.75 

57.3 

120 

23.43 

28.12 

31.25 

37.5 

35.15 

42.18 

39.06 

46.87 

42.96 

51.56 

I) 

|  =  0.375 

•&  =  0.4375 

J-0.5 

&  =  0.5625 

f  =  0.625 

36 

156.2 

187.5 

182.3 

218.8 

208.3 

250. 

234.3 

281.2 

260.4 

312.5 

38 

148. 

177.6 

172.6 

207.1 

197.2 

236.6 

221.8 

266.2 

246.6 

296. 

40 

140.6 

168.7 

164. 

196.8 

187.4 

224.9 

210.8 

253. 

234.4 

281.2 

42 

133.9 

160.7 

156.1 

187.4 

178.4 

214. 

200.8 

241. 

223.2 

267.8 

44 

127.8 

153.4 

148.9 

178.7 

170. 

204.5 

191.7 

230. 

213. 

255.6 

48 

117.2 

140.6 

136.7 

164. 

156.2 

187.4 

165.7 

198.9 

195.3 

234.4 

54 

104.2 

125. 

121.5 

145.8 

138.9 

166.6 

156.2     187.5 

173.6 

208.4 

60 

93.75 

112.5 

109.4 

131.1 

125. 

150. 

140.6 

168.7 

156.2 

187.5 

66 

85.2 

102.2 

99.45 

119.3 

113.7 

136.3 

127.9 

153.4 

142. 

170.4 

72 

78.12 

93.74 

91.06 

109.3 

104. 

124.8 

117.1 

140.5 

130.2 

156.2 

78 

72.1 

86.53 

85.39 

102.4 

98.68 

117.7 

109.3 

131.2 

120. 

144.2 

84 

66.96 

80.35 

78.12 

93.74 

89.28 

107.1 

100.4 

120.5 

111.6 

133.9 

90 

62.5 

75. 

72.91 

87.5 

83.33 

100. 

93.7 

112.4 

104. 

125. 

96 

58.58 

70.29 

68.29 

81.95 

78. 

93.6 

87.8 

105.4 

97.6 

117.2 

102 

55.12 

66.14 

64.32 

77.19 

73.53 

88.22 

82.7 

99.2 

91.9 

110.31 

108 

52.1 

62.5 

60.77 

72.93 

69.45 

83.3 

78.1 

93.7 

86.8 

104.2 

120 

46.87 

56.25 

54.68 

65.62 

62.5 

75. 

70.3 

84.3 

78.1 

93.7 

STRENGTH    OF   STEAM-BOILERS. 


93 


1 

TABLE  XVIII. 

Boiler  Plates  Stamped  5O.OOO  Ibs.    Safety-strain  J  «=  8333.3. 

-3J 

Thickness  of  boiler-plate  in  fractions  of  an  inch. 

S| 

o>  ""' 

&=  0.1875 

£  =  0.25 

&  =0.28125 

^  =  0.3125 

ft  =  0.34375 

II 

Riveting. 

Hiveting. 

Riveting. 

Riveting. 

Riveting. 

ll 

Single. 

Double. 

-Miml.'.    Double. 

Single. 

Double. 

Single. 

Double. 

Single. 

Double. 

D 

Pressures. 

1'ressiires. 

Pressures. 

Pressures. 

Pressures. 

36 

86.8 

104.2 

115.7 

138.9 

130.2 

156.2 

144.7 

173.6 

159.1 

191. 

38 

82.23 

98.68 

109.6 

131.5 

123.3 

148. 

137. 

164.5 

150.7 

180.8 

40 

78.12 

93.74 

104.1 

125. 

117.1 

140.6 

130.2 

156.2 

143.2 

171.8 

42 

74.49 

89.38 

99.2 

119. 

111.6 

133.9 

124. 

148.8 

136.4 

163.7 

44 

71.    ' 

85.2 

94.69 

113.6 

106.5 

127.7 

118.4 

142. 

130.2 

156.2 

48 

65.1 

78.12 

86.8 

104.1 

97.4 

116.9 

108. 

130.2 

119.1 

142.9 

54 

57.62 

69.44 

77.16 

92.59 

86.8 

104.1 

96.45 

115.7 

101. 

121.3 

60 

52. 

62.4 

69.44 

83.33 

78.12 

93.74 

86.8 

104.1 

95.45 

114.5 

66 

47.34 

56.8 

63.13 

75.75 

71.02 

85.22 

78.91 

94.69 

86.8 

104.1 

72 

43.4 

52. 

57.87 

69.44 

65.11 

78.13 

72.35 

86.8 

79.57 

95.48 

*-0 

/8 

40. 

48. 

53.67 

64.4 

60.22 

72.26 

66.77 

80.12 

73.44 

88.13 

84 

37.2 

44.64 

49.6 

59.5 

55.8 

66.96 

62. 

74.4 

68.2 

81.84 

90 

34.72 

41.66 

46.29 

55.55 

52.08 

62.5 

57.87 

69.44 

63.65 

76.38 

96 

32.55 

39. 

43.4 

52. 

48.82 

58.59 

54.25 

65.1 

59.67 

71.61 

102 

30.63 

36.77 

40.66 

48.79 

45.87 

55.04 

51.08 

61.29 

56.17 

67.41 

108 

28.81 

34.72 

38.58 

46.29 

43.4 

52.08 

48.22 

57.85 

53.03 

63.63 

120 

26. 

31.2 

34.72 

41.66 

39.06 

46.87 

43.4 

52.08 

47.74    57.29 

D 

|  =  0.375 

^=0.4375 

|  =  0.5 

ffe  =  0.5625 

|  =  0.625 

36 

173.6 

208.3 

202.5 

243. 

231.5 

277.8 

260.4 

312.4 

289.4 

347.2 

38 

164.4 

197.3 

191.8 

230.2 

219.3 

263.1 

246.6 

296. 

274. 

329. 

40 

156.2 

187.5 

182.2 

218.7 

208.3 

250. 

234.2 

281.2 

260.4 

312.4 

42 

148.8 

178.6 

173.6 

208.3 

198.4 

238. 

223.2 

267.8 

248. 

297.6 

44 

142. 

170.4 

165.7 

198.8 

189.4 

227.3 

213. 

255.4 

236.8 

284. 

48 

130.2 

156.2 

151.9 

182.3 

173.6 

208.3 

194.8 

233.8 

216. 

260.4 

54 

115.7 

138.9 

135. 

162. 

154.3 

185.2 

173.6 

208.2 

192.9 

231.4 

60 

104.1 

125. 

121.5 

145.8 

138.9 

166.6 

156.2 

187.5 

173.6 

208.2 

66 

94.69 

113.6 

110.4 

132.5 

126.2 

151.5 

142. 

170.4 

157.8 

189.4 

72 

86.8 

104.1 

101.2 

121.5 

115.7 

138.9 

130.2 

156.2 

144.7 

173.6 

78 

80.12 

96.15 

93.71 

112.4 

107.3 

128.8 

120.4 

144.5 

133.5 

160.2 

84 

74.4 

89.28 

86.8 

104.1 

99.2 

119. 

111.6 

133.9 

124. 

148.8 

90 

69.44 

83. 

81.01 

97.21 

92.58 

111.1 

104.1 

125. 

115.7 

138.9 

96 

65.1 

78.2 

75.95 

91.14 

86.8 

104. 

97.64 

117.2 

108.5 

130.2 

102 

61.27 

73.54 

71.29 

85.55 

81.32 

97.58 

91.74 

110.1 

102.1 

122.6 

108 

57.85 

69.45 

67.5 

81. 

77.15 

92.6 

86.8 

104.1 

96.44 

115.7 

120 

52.08 

62.49 

60.76 

72.92 

69.44 

83.33 

78.12 

93.74 

86.8 

104.1 

11} 


STEAM  ENGINEERING. 


TABLE  XIX. 

Boiler  Plates  Stamped  55.OOO  Ibs.     Safety-strain  \  -  9166.6. 

°J 

Thickness  of  boiler-plate  in  fraction*  of  ai 

i  inch. 

ll 

A-  0.1875 

$  =  0.25 

&  =  0.28125 

^  =  0.3125 

\\  =  0.34375 

s  •- 

Riveting. 

Riveting. 

Riveting. 

Riveting. 

Riveting. 

n 

Single.  |  Double. 

Single. 

Double. 

Single. 

Double. 

Single. 

Double. 

Single.  Double. 

D 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

36 

95.48 

114.6 

127.3 

152.8 

143.2 

171.8 

159.1 

190.9 

175. 

210. 

38 

90.46 

108.5 

120.6 

144.7 

135.6 

162.7 

150.7 

180.9 

165.8 

198.9 

40 

85.93 

103.1 

114.6 

137.5 

128.9 

154.7 

143.2 

171.9 

157.5 

189. 

42 

81.84 

98.2 

109.1 

130.9 

122.7 

147.3 

136.4 

163.7 

150. 

180.1 

44 

78.12 

93.74 

104.1 

125. 

117.1 

140.6 

130.2 

156.2 

143.2 

171.8 

48 

71.61 

85.93 

95.43 

114.6 

107.4 

128.8 

119.3 

143.2 

131.2 

157.5 

54 

63.65 

76.38 

84.87 

101.8 

95.4 

114.5 

106. 

127.3 

116.6 

140. 

60 

57.29 

68.74 

76.38 

91.65 

85.93 

103.1 

95.48 

114.6 

105. 

126. 

66 

52. 

62.4 

69.44 

83.32 

78.12 

93.74 

86.8 

104.1 

95.45 

114.5 

72 

47.74 

57.28 

63.65 

7%.38 

71.6 

85.92 

79.56 

95.48 

87.52 

105. 

78 

44. 

52.8 

58.76 

70.51 

66.1 

79.32 

73.45 

88.13 

80.79    96.95 

84 

40.92 

49.1 

54.56 

65.47 

61.38 

73.65 

68.2 

81.84 

75.02 

90.02 

90 

38.19 

45.82 

50.92 

61.1 

57.28 

68.73 

63.65 

76.38 

70.01 

84.02 

96 

35.8 

42.96 

47.74 

57.28 

53.7 

64.44 

59.67 

71.61 

65.64 

78.77  ! 

102 

33.7 

40.44 

44.93 

53.9 

50.54 

60.65 

56.16 

67.39 

61.78 

74.13 

108 

31.82 

38.19 

42.43 

50.9 

47.71 

57.26 

53. 

63.65 

58.32 

69.99   ! 

120 

28.64 

34.37 

38.19 

45.82 

42.96 

50.56 

47.74 

57.29 

52.51  i  63.02  '' 

D 

1=0.375 

A-  0-4375 

I-  0.5 

^  =  0.5625 

|  =  0.625       i 

36 

190.9 

229.1 

•2-2-2.7 

267.3 

254.6 

305.5 

286.4 

343.6 

318.2 

381.8 

38 

180.9 

217. 

217. 

253.2 

241.2 

289.4 

271.2 

325.4 

301.4 

361.8 

40 

171.9 

206.2 

200. 

240. 

229.1 

275. 

257.8 

309.4 

286.4 

343.8 

42 

163.7 

196.4 

190.9    229.1 

218.2 

261.9 

245.4 

294.6 

•27-2.S    327.4 

44 

156.2 

187.5 

182.2    218.6 

208.3 

250. 

234.2 

281.2 

260.4    312.4 

48 

143.2 

171.8 

167.1    199.5 

190.9 

229.1 

214.8 

257.6 

238.6 

286.4 

54 

127.3 

152.7 

148.5 

178.2 

169.7 

203.7 

190.8 

229 

212. 

254.6 

60 

114.6 

137.5 

133.7 

160.4 

152.7 

183.3 

171.8 

206.2 

190.9 

229.2 

66 

104.1 

125. 

121.4 

145.7 

138.9 

166.6 

156.2 

187.5 

173.6 

208.2 

72 

95.48 

114.5 

111.4 

133.6 

127.3 

152.7 

143.2 

171.8 

159.1 

190.9 

78 

88.13 

105.7 

102.7 

123.3 

117.5 

141. 

132.2 

158.6 

146.9 

176.2 

84 

81.84 

982 

95.48 

114.6 

109.1 

130.9 

122.7 

147.3 

136.4 

163.7 

90 

76.38 

91.65 

89.11 

106.9 

101.8    122.2 

114.5 

137.4 

127.3 

152.7 

96 

71.61 

85.93 

83.54 

100.2 

95.48  1  114.5 

107.4 

128.9 

119.3 

143.2 

102 

67.4 

80.88 

78.33 

94. 

89.87    107.8 

101.1 

121.3 

112.3 

134.7 

108 

63.65 

76.35 

74.25      89.1 

84.85    101.8 

95.42 

114.5 

106. 

127.3 

120 

57.29 

68.74 

66.83 

80.2 

76.38    91.64 

89.92 

101.1 

95.5 

114.6 

STRENGTH    OF    STEAM-HOI  l.KRS. 


95 


TABLE  XX. 
Boiler  Plates  Stamped  6O.OOO  Ibs.     Safety-strain  \  =  1O.OOO. 


c| 

Thickness  of  boiler-plate  in  fractions  of  tin  inch. 

^  = 

c  •" 

&=  0.1  875 

J  =  0.25 

&  =  0.28125 

&  =  0.3125 

J  £  =  0.34375 

r  £ 

Riveting. 

Riveting. 

Riveting. 

Riveting. 

Riveting. 

^ 

Single. 

Double. 

Single. 

Double. 

Single. 

Double. 

Single.  |  Double. 

Single.  |  Double. 

D 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

36 

104.1 

125. 

138.9 

166.6 

156.2 

187.5 

173.6 

208.3 

190.9 

229.1 

38 

98.68 

118.4 

131.6 

157.9 

148. 

177.6 

164.5 

197.3 

180.9 

217.1 

40 

93.74 

112.5 

125. 

150. 

140.7 

168.9 

156.2 

187.4 

166.8 

200.1 

42 

89.28 

107.1 

119. 

142.8 

133.8 

160.6 

148.7 

178.6 

163.6 

196.4 

44 

85.22     102.2 

113.6 

136.3 

127.8 

153.3 

142.' 

170.4 

156.2 

187.4 

48 

78.12 

93.74 

104.1 

125. 

117.1 

140.6 

130.2 

156.2 

143.2 

171.8 

54 

69.44 

82.44 

92.59 

110.1 

104.1 

125.. 

115.7 

138.9 

127.3 

152.7 

GO 

62.4 

75. 

83.33 

100. 

93.71 

113.4 

104.1 

125. 

114.5 

137.4 

66 

56.8 

68.1 

75.75 

90.9 

85.22 

102.2 

94.69 

113.6 

104.1 

125. 

72 

52. 

62.4 

69.44 

83.32 

78.12 

93.74 

86.8 

104.1 

95.45 

114.5 

T8 

48. 

57.6 

64.4 

76.92 

72.26 

86.71 

80.12 

96.15 

88.13 

105.7 

84 

44.64 

53.52 

59.5 

71.4 

66.95 

80.34 

74.4 

89.28 

81.84 

98.21 

90 

41.66 

50. 

55.55 

66.66 

62.49 

75. 

69.44 

83.33 

76.38 

91.66 

90 

39. 

46.8 

52. 

62.4 

58.55 

70.26 

65.1 

78.12 

71.61 

85.93 

102 

36.76 

44.12 

49.02 

58.8 

55.14 

66.17 

61.27 

73.51 

67.4 

80.88 

108 

34.72 

41.22 

46.29 

55.05 

52.07 

62.48 

57.85 

69.45 

63.65 

76.38 

120 

32.2 

37.5 

41.661  50. 

46.87 

56.24 

52.08 

62.5 

57.29 

68.75 

D 

|  =  0.375 

^  =0.4375 

J  =  0.5 

&  =  0.5625 

f  =  0.625 

36 

208.3 

250. 

242. 

290.4 

277.8 

333.3 

312.4 

375. 

347.2 

416.6 

38 

197.3 

237. 

230.3 

276.3 

263.1 

315.8 

296. 

355.2 

329. 

394.6 

40 

187.4 

225. 

218.7 

242.5 

250. 

300. 

281.4 

337.8 

312.4 

374.8 

42 

178.6 

214.3 

208.3 

249.9 

238. 

285.6 

267.6 

321.2 

297.4 

357.2 

44 

170.4 

204.5 

198.8 

238.6 

227.2 

272.7 

255.6 

306.6 

284. 

340.8 

48 

156.2 

187.5 

182.2 

218.6 

208.3 

250. 

234.2 

281.2 

260.4 

312.4 

54 

138.9 

165.7 

162. 

194.4 

185.2 

220.2 

208.2 

250. 

231.4 

277.8 

60 

125. 

150. 

145.7 

174.9 

166.6 

200. 

187.4 

226.8 

208.2 

250. 

66 

1136 

136.3 

132.5 

159. 

151.5 

181.8 

170.4 

204.4 

189.4 

227.2 

72 

104.1 

125. 

121.4 

145.7 

138.9 

166.6 

156.2 

187.5 

173.6 

208.2 

78 

96.15 

115.8 

112.4 

134.9 

128.8 

153.8 

144.5 

173.4 

160.2 

192.3 

84 

89.28 

107.1 

104.1 

124.9 

119. 

142.8 

133.9 

160.7 

148.8 

178.5 

90 

83.33 

100. 

97.21 

116.6 

111.1 

133.3 

125. 

150. 

138.9 

166.6 

96 

78.12 

93.74 

91. 

109.2 

104. 

124.8 

117.1 

140.5 

130.2 

156.2 

102 

73.53 

88.23 

85.78 

102.9 

98.04 

117.6 

110.3 

132.3 

122.5 

147. 

108 

69.45 

82.85 

81.01 

97.21 

92.6 

110.1 

104.1 

124.9 

115.7 

138.9 

120 

62.5 

75. 

73.86 

8863 

83.33 

100. 

93.74 

112.5 

104.1 

125. 

96 


STEAM  ENGINEERING. 


TABLE  XXI. 

Boiler  Plates  Stamped  65.OOO  Ibs.     Safety-strain  £=10833.  3. 

*J 

Thickness  of  boiler-plate  in  fractions  of  an  inch. 

r-S 

T^  =  0.1875 

£  =  0.25 

&  =  0.28125 

&  =  0.3125 

\%  =  0.34375 

1| 

Riveting. 

Riveting. 

Riveting. 

Riveting. 

Riveting. 

«J 

Single. 

Double. 

Single. 

Double. 

Single. 

Double. 

Single.  1  Double. 

Single. 

Double. 

D 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

36 

112.8 

135.4 

150.4 

180.5 

169.2 

203. 

188. 

225.6 

206.8 

248.1 

38 

106.9 

128.3 

142.5 

171. 

160.3 

192.4 

178.2 

213.8 

196. 

235.2 

40 

101.5 

121.8 

135.4 

162.5 

152.3 

182.8 

169.3 

203.1 

186.2 

223.4 

42 

96.72 

116. 

128.9 

154.7 

145. 

174. 

161.2 

193.5 

177.3 

212.8 

44 

92.32 

110.8 

123'.! 

147.7 

138.5 

166.2 

153.9 

184.7 

169.3 

203.1 

48 

84.63 

101.5 

112.8 

135.4 

126.9 

152.3 

141. 

169.3 

155.1 

186.3 

54 

75.21 

90.25 

100.3 

120.3 

112.8 

135.4 

125.4 

150.4 

137.9 

165.5 

60 

67.7 

81.24 

90.27 

108'.3 

101.5 

121.8 

112.8 

135.4 

124.1 

148.9 

66 

61.55 

73.86 

82. 

98.4 

92.3 

110.7 

102.6 

123.1 

112.8 

135.4 

72 

56.42 

67.7 

75.22 

90.26 

84.61 

101.5 

94. 

112.8 

103.4 

124.1 

78 

52. 

62.4 

69.44 

83.33 

78.12 

93.74 

86.8 

104.1 

95.45 

114.5 

84 

48.36 

58. 

64.48 

77.37 

72.54 

87.05 

80.6 

96.72 

88.66 

106.4 

90 

45.13 

54.15 

60.18 

72.21 

67.69 

81.23 

75.2 

90.24 

82.72 

99.26 

96 

42.31 

50.77 

56.37 

67.64 

63.44 

76.13 

70.52 

84.63 

77.57 

93.09 

102 

39.82 

47.75 

53.1 

63.72 

59.73 

71.68 

66.37 

79.65 

73.01 

87.61 

108 

37.61 

45.12 

50.15 

60.15 

56.42 

67.71 

64.7 

75.2 

68.95 

82.74 

120 

38.85 

40.62 

45.13 

54.16 

50.77 

60.93 

56.42 

67.71 

62.06 

74.48 

D 

|=0.375 

^=0.4375 

J  =  0.5 

&=  0.5625 

f  =  0.625 

36 

225.6 

271. 

263.2 

315.8 

300.8 

360.9 

338.4    406. 

376. 

451.2 

38 

213.8 

256.6 

249.4 

299.3 

285.1 

342. 

320.6    384.8 

356.4 

427.6 

40 

203.1 

243.8 

236.9 

284.3 

270.1 

325. 

304.6    365.6 

338.6 

406.2 

42 

193.5 

232.2 

225.6 

270.7 

257.9 

309.5 

290.      348. 

322.4 

387. 

44 

184.7 

221.6 

215.4 

258.5 

246.2 

295.4 

277.      332.4 

307.8 

369.4 

48 

169.3 

203.1 

197.4 

236.9 

225.7 

270.8 

253.8    304.6 

282. 

338.6 

54 

150.4 

180.6 

175.5 

210.6 

200.6 

240.7 

225.6    270.8 

250.8 

300.8 

60 

135.4 

162.5 

158. 

189.5 

180.5 

216.6 

203. 

243.6 

225.6 

270.8 

66 

123.1 

147.7 

143.5 

172.2 

164. 

196.8 

184.6 

221.4 

205.2 

246.2 

72 

112.8 

135.4 

131.6 

157.9 

150.4 

180.5 

169.2    203. 

188. 

225.6 

78 

104.1 

125. 

121.4 

145.7 

138.9 

166.6 

156.2 

187.5 

173.6 

208.2 

84 

96.72 

116. 

112.8 

135.4 

128.9 

154.7 

145.1 

174.1 

161.2 

193.4 

90 

90.24 

108.3 

105.3 

126.4 

120.3 

144.4 

135.4 

162.4 

150.4 

180.5 

96 

84.63 

101.5 

98.68 

118.4 

112.7 

135.3 

126.9 

152.2 

141.0 

169.2 

102 

79.65 

95.5 

92.92 

111.6 

106.2 

127.4 

119.4 

143.3 

132.7 

159.3 

108 

75.2 

90.3 

87.76 

105.3 

100.3 

120.3 

112.8 

135.4 

125.4 

150.4 

120 

67.71 

81.25 

83.98 

100.8 

90.26 

108.3 

101.5 

121.8 

112.8 

1-35.4 

STRENGTH    OF   STEAM-BOILERS. 


97 


TABLE  XXII. 

Boiler  Plates  Stamped  7O.OOO  Ibs.    Safety-strain  J  =  11666.6. 

oj 

(-.Tt 

Thickness  of  boiler-plate  in  fractions  of  an  inch. 

SJ 

&=  0.1875 

£  =  0.25 

&  =  0.28125 

^  =  0.3125 

&  =  0.34375 

Ijj 

Riveting. 

Eiveting. 

Riveting. 

Riveting. 

Riveting. 

"1 

Single. 

Double. 

Single.  |  Double. 

Single. 

Double. 

Single. 

Double. 

Single. 

Double. 

D 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

Pressures. 

36 

121.5 

145.8 

164.2  j  197.1 

183.3 

220. 

202.5 

243. 

222.7 

267.5 

38 

116. 

139.2 

153.5 

184.2 

172.7 

217.2 

191.9 

230.2 

211. 

253.2 

40 

109.3 

131.2 

145.8 

174.9 

164. 

196.8 

182.3 

218.7 

200.5 

240.6 

42 

104.1 

125. 

138.9 

166.6 

156.2 

187.5 

173.6 

208.3 

190.9 

229.1 

44 

99.42 

119.3 

132.5 

159. 

149.1 

178.9 

165.7 

198.8 

182.2 

218.7 

48 

91.13 

109.3 

121.5 

145.3 

136.7 

164. 

151.9 

182.3 

167.1 

200.5 

54 

81. 

97.2 

108. 

129.6 

121.5 

145.8 

135. 

162. 

148.5 

178.2 

60 

72.9 

87.48 

97.2 

116.6 

109.3 

131.2 

121.5 

145.8 

133.6 

160.4 

66 

66.3 

79.56 

88.37 

106. 

99.43 

119.3 

110.5 

132.5 

121.5 

145.8 

72 

60.75 

72.9 

81. 

97.2 

91.1 

109.3 

101.2 

121.5 

111.3 

133.6 

78 

56.1 

67.32 

74.7 

89.64 

80.39 

96.47 

93.47 

112.2 

102.8 

123.4 

84 

52. 

62.4 

69.4 

83.28 

78.1 

93.72 

86.8 

104.1 

95.45 

114.5 

90 

48.6 

58.32 

64.8 

77.77 

72.9 

87.48 

81. 

97.2 

89.1 

106.9 

96 

45.5 

54.6 

60.8 

72.96 

68.37 

82.05 

75.95 

91.14 

83.54 

101.2 

102 

42.9 

51.3 

57.2 

68.6 

64.35 

77.22 

71.5 

85.8 

78.65 

94.38 

108 

40.5 

48.6 

54. 

64.8 

60.75 

72.9 

67.5 

81. 

74.25 

89.1 

120 

36.45 

43.74 

48.6 

58.32 

54.68 

65.61 

60.76 

72.9 

66.83 

80.2 

D 

|  =  0.375 

^  =  0.4375 

|  =  0.5 

&  =  0.5625 

|=0.625 

36 

243 

291.6 

285.7 

342.9 

328.5 

394.2 

366.6 

440. 

405. 

486. 

38 

230.2 

276.3 

269.5 

323.4 

307. 

368.4 

345.4 

434.4 

383.8 

460.4 

40 

218.7 

262.4 

255.1 

306.1 

291.6 

349.9 

328. 

393.6 

364.6 

437.4 

42 

208.3 

250. 

243. 

291.6 

277.7 

333.3 

312.4 

375. 

347.2 

416.6 

44 

198.8 

238. 

231.9 

278.3 

265. 

318. 

298.2 

357.8 

331.4 

397.6 

48 

182.3 

218.7 

212.6 

255.1 

243. 

290.6 

273.4 

328. 

303.8 

364.6 

54 

162. 

194.4 

189. 

226.8 

216. 

259.2 

243. 

291.6 

270. 

324. 

60 

145.8 

175. 

170.1 

204.1 

194.4 

233.3 

218.6 

262.4 

243. 

291.6 

66 

132.5 

159. 

154.7 

185.6 

176.7 

212. 

198.8 

238.6 

221. 

265. 

72 

121.5 

145.8 

141.7 

170.1 

162. 

194.4 

182.2 

218.6 

202.4 

243. 

78 

112.2 

134.6 

130.8 

156.9 

149.4 

179.3 

160.8 

192.9 

186.9 

224.4 

84 

104.1 

125. 

121.4 

145.7 

138.8 

166.6 

156.2 

187.4 

173.6 

208.2 

90 

97.2 

116.6 

113.4 

136.1 

129.6 

155.5 

145.8 

174.9 

162. 

194.4 

96 

91.14 

.109.3 

106.3 

127.5 

121.6 

145.9 

136.7 

164.1 

151.9 

182.3 

102 

85.8 

102.6 

100.1 

120.1 

114.4 

137.2 

128.7 

154.4 

143. 

171.6 

108 

81. 

97.2 

94.5 

113.4 

108. 

129.6 

121.5 

145.8 

135. 

162. 

120 

72.9 

87.5 

85.05 

102. 

97.2 

116.6 

109.3 

131.2 

121.5 

145.8 

98  STEAM  ENGINEERING. 


STRENGTH  OF  BOILER-SHELLS. 

§  74.  The  steam-pressure  per  square  inch  in  the  boiler,  multiplied 
by  the  inside  diameter  of  the  shell  in  inches,  is  the  strain  on  the 
plates  per  inch  of  length  of  the  shell ;  and  as  this  strain  is  borne  by 
two  sides  of  the  shell,  only  one-half  of  it  is  borne  by  each  side. 

£  =  ultimate  strength  in  pounds  per  square  inch  of  section  of  the 

plate. 

t  =  thickness  of  the  plate  in  fractions  of  an  inch. 
D  =  inside  diameter  of  the  boiler  in  inches. 
p  =  steam-pressure  in  pounds  per  square  inch  above  that  of  the 

atmosphere. 


g  75.  Ultimate  Strength  of  Solid  Shell  without  Riveted  Joints. 

2  t  S 
Steam-pressure,  p  = 9 

9  /  Sf 
Diameter  of  boiler,      D  = .10 


Thickness  of  plate,        t  -=  —  ^  ......     11 


Breaking-strain,  S=—   ......     12 


|  76.  Safety  Strength  of  Solid  Shell  without  Riveted  Joints  (J  of  the 
Ultimate  Strength). 

±  c 
Steam-pressure,  p  =  — — , 13 

*    O 

Diameter  of  boiler,      D  = .     .        .        .        .        .14 

2p 

2  /)» 
Thickness  of  plate,        t  = -.         .        .        .        .15 

Breaking-strain,          .  S= ^ 16 


STRENGTH  OF  RIVETED  JOINTS.  99 

STRENGTH    OF   SINGLE-RIVETED   JOINTS. 

§  77.  The  post-office  engineers  pierce  the  sheets  of  post-stamps  with 
small  holes  around  each  stamp  in  order  to  make  the  sheet  tear  easily  for 
separating  the  stamps.  This  is  a  practical  illustration  of  the  effect  of 
punching  holes  in  the  boiler-plates  for  the  riveted  joints.  The  plate 
is  weakened  in  proportion  as  the  diameter  of  the  rivet  is  to  the  dis- 
tance between  the  centres  of  rivets.  Suppose  the  diameter  of  the  rivet 
to  be  d  =  1  and  distance  between  centres  D  =  3,  then  the  strength  of 
the  solid  plate  is  to  that  of  the  punched  plate  as 


D  3 

That  is,  the  strength  of  the  punched  plate  is  only  66  per  cent.,  or  § 
of  that  of  the  solid  plate. 

The  static  condition  of  riveted  joints  is  that  the  sheering  strain  on 
the  rivet  is  equal  and  opposite  to  the  tearing  strain  on  the  plate,  and 
the  strength  to  resist  these  two  strains  must  therefore  be  alike  for  the 
greatest  strength  of  the  joint. 

*It  has  been  found  by  experiments  that  the  sheering  and  tearing 
strength  of  wrought  iron  are  nearly  alike  per  section  strained,  and 
the  slight  difference  varies  either  way  according  to  the  particular  iron 
experimented  upon,  but  on  an  average  the  sheering  strength  appears 
to  have  some  advantage  over  that  of  tearing. 

Assuming  these  two  strengths  to  be  alike,  the  section  of  the  rivet 
should  be  equal  to  the  section  of  the  plate  between  the  rivets. 

d  =  diameter  of  the  rivet. 

d  =  distance  between  centres  of  rivets. 

t  =  thickness  of  plate. 

Areas  of  sections,  0.7854  d2  =  t  (3  -  d).  8  =  -  (0.7854  d  +  f). 

The  proportion  between  d  and  t  averages  in  practice  2  t  =  d  —  that 
is,  the  diameter  of  the  rivet  is  made  twice  the  thickness  of  the  plate. 
For  thin  plates  the  diameter  of  the  rivet  is  made  larger,  and  for  thick 
plates  smaller,  than  d  =  2  t,  as  will  be  seen  in  the  accompanying  table, 
which  is  set  up  from  practice. 

Assuming  that  d  =  2  t  or  t  =  0.5  d,  which,  inserted  for  t  in  the  above 
formula,  will  give  the  proportion  between  d  and  3  —  namely, 

0.7854  d1  =  0.5  d(8-d)      and      0.5824  d  =  0.5  (8  -  d). 

Distance  d  =  2.57  d  between  centres  of  rivets. 

This  is  the  proportion  of  3  and  d,  as  used  in  practice  for  1-inch 
plate,  but  the  diameter  of  the  rivet  is  then  made  much  less  than  2  t. 


100  STEAM  ENGINEERING. 


The  punching  of  holes  in  the  boiler-plate  disturbs  the  fibres  for 
some  distance  around  the  hole,  and  thus  diminishes  the  strength,  so 
that  the  section  between  the  rivets  is  weaker  than  an  equal  section 
of  the  same  plate  not  punched.  This  weakening  amounts  to  from  10 
to  20  per  cent.,  according  to  experiment,  with  different  kinds  of  iron. 
Allowing  37  per  cent,  of  section  punched  away  by  the  hole  and  13 
per  cent,  for  disturbing  the  fibres  by  punching,  there  remains  only  50 
per  cent,  of  strength  of  the  solid  plate  in  the  single-riveted  joint  to  Be 
relied  upon  for  safety  in  practice. 

Experiments  with  strength  of  single-riveted  joints  have  given  as 
high  as  70  per  cent,  of  that  of  the  solid  plate ;  but  the  writer  is  not 
disposed  to  rely  upon  those  experiments  in  practice  of  boiler-making, 
for  which  reason  only  50  per  cent,  is  allowed  in  the  following  formulas. 

§  78.  Bursting  Strength  of  Single-riveted  Joints  in  Boiler-shells. 
Notation  of  letters  is  the  same  as  before  repeated. 

Steam-pressure,  p  =  — 17 

Diameter  of  boiler,          D  =  — 18 

P 

Thickness  of  plate,  t  =  — £ 19 

Breaking-strain,  S=  — - 20 

The  safety  strength  of  materials  should  not  be  taken  more  than  25 
per  cent,  of  the  ultimate  strength. 

I  79.  Safety  Strength  of  Single-Riveted  Joints  with  Punched  Holes 
in  Boiler  Shells. 

•   O 

Steam-pressure,  »  =  — 21 

4Z> 

i  W 

Diameter  of  boiler,          D  = .         .  22 

4p 

Thickness  of  plate, 

Breaking-strain,  8=^  ^ F          ....        24 


STRENGTH  OF  RIVETED  JOINTS.  101 

Example.  A  steam-boiler  of  D  =  147  inches  diameter  is  to  carry 
jo  =  60  pounds  steam-pressure,  and  the  thickness  of  plates  £  =  f  of  an 
inch.  Required  what  stamp  the  plates  must  have  ? 


The  breaking-strain  of  the  iron  plates  should  be  54096  pounds  to 
the  square  inch.  By  the  government  rule,  Formula  4,  the  stamp 
need  only  be  40572. " 

§  80.  The  government  rule  allows  the  boilers  to  be  25  per  cent, 
weaker  than  by  Formulas  21  to  24  inclusive.  It  is  difficult  to  guard 
against  all  carelessness  in  boiler-making.  When  the  holes  in  the 
plates  are  not  punched  to  properly  match  one  another,  they  form  an 
eccentric  opening,  through,  which  a  drift  is  driven  to  make  the  holes 
concentric.  This  drift  does  not  only  overstrain  the  iron,  but  inclines 
the  hole  so  that  the  rivet  will  not  be  at  right  angles  to  the  plate.  The 
strength  of  such  a  rivet  may  be  only  20  per  cent,  of  that  of  a  properly 
riveted  hole.  It  is  almost  impracticable  to  punch  the  holes  in  boiler- 
plates sufficiently  correct  to  match  one  another,  as  required  for  proper 
work.  The  strength  of  single-riveted  joints  with  punched  holes  should 
therefore  not  be  taken  over  50  per  cent,  of  that  of  the  solid  plate. 

For  drilled  holes  known  to  be  well  fitted,  60  per  cent,  may  be  trusted 
upon  for  single-riveted  joints. 

g  81.   Safety  Strength  of  Single-riveted  Joints  with  Drilled  Holes 
in  Boiler  Shells. 

25 
26 

27 

28 

§  82.  It  is  impracticable  to  proportion  the  riveted  joints  so  perfectly 
that  the  shearing  strength  of  the  rivet  be  equal  to  the  tearing  strength 
of  the  plate,  for  the  actual  strength  of  the  iron  varies  more  than  does 
the  proportion  of  dimensions  of  the  joint. 


0.3  tS 

P        D      ' 

D_Mt8 

P 

Thickness  of  plate, 
Break  in  er-strain. 

5  =  O3S    

102 


STEAM  ENGINEERING. 


The  following  table  gives  the  proportions  of  single-riveted  joints  to 
the  nearest  16th  of  an  inch  as  used  in  practice. 

It  will  be  seen  in  the  table  that  the  section  of  the  plate  between  the 
rivets  is  greater  than  the  section  of  the  rivet,  except  for  one-eighth  of 
an  inch  plate. 

For  drilled  holes  make  the  distance  between  the  centres  of  the  rivets 
one-eighth  (£)  of  an  inch  less  than  that  for  punched  holes. 

TABLE  XXIII. 
Proportion  of  Single-riveted  Lap-joints  with  Punched  Holes. 


Thickness 
of  plate. 

Riv 
Diameter. 

ets. 
Length. 

Distance 
betw.  cent. 

Lap  of 
joint. 

Area  of 
rivet. 

Area  of 
plate. 

Per  cent, 
of  solid 

t 

d 

/ 

6 

inches. 

sq.  inch. 

sq.  inch. 

plate. 

1/8 

5/16 

1/2 

7/8 

1.1/4 

0.0767 

0.07031 

64 

3/16 

7/16 

3/4 

1.5/16 

1.1/2 

0.1503 

0.16406 

66 

1/4 

1/2 

1.1/8 

1.1/2 

1.3/4 

0.1963 

0.25000 

66 

5/16 

5/8 

1.3/8 

1.7/8 

2  in. 

0.3067 

0.39062 

66 

3/8 

3/4 

1.11/16 

2.1/4 

2.1/4 

0.4417 

0.56250 

66 

7/16 

13/16 

1.15/16 

2.3/8 

2.3/8 

0.5184 

0.68359 

65 

1/2 

7/8 

2.1/4 

2.1/2 

2.1/2 

0.6013 

0.75250 

64 

9/16 

lin. 

2.1/2 

2.5/8 

2.5/8 

0.7854 

0.91406 

63 

5/8 

1.1/16 

2.13/16 

2.3/4 

2.7/8 

0.8904 

1.05468 

62 

11/16 

1.1/8 

3.1/8 

2.7/8 

3.1/8 

0.9940 

1.03125 

61 

3/4 

1.3/16 

3.5/8 

3  in. 

3.3/8 

1.3603 

1.35937 

60 

13/16 

1.5/16 

3.11/16 

3.1/4 

3.5/8 

1.3605 

1.57422 

60 

7/8 

1.3/8 

3.15/16 

3.1/2 

4  in. 

1.4840 

1.85937 

60 

15/16 

1.1/2 

4.1/4 

3.3/4 

4.1/4 

1.767 

2.10937 

60 

lin. 

1.5/8 

4.1/2 

4  in. 

4.5/8 

2.073 

2.375 

60 

DOUBLE-RIVETED   LAP-JOINTS. 

§  83.  Double-riveted  joints,  if  properly  proportioned,  increase  the 
strength  of  the  boiler  about  40  per  cent,  on  account  of  the  rivets  being 
spaced  farther  apart,  leaving  more  section  of  plate  between  them  to 
resist  the  strain.  The  rivets  are  arranged  in  two  rows,  zig-zag,  over 
one  another,  as  shown  in  the  accompanying  illustration.  For  the 
greatest  strength  the  distance  between  the  rivets  in  the  direction  of 
the  joint  should  be  double  the  distance  between  the  centre  lines  of 
the  two  rows,  and  the  rivets  will  then  form  a  right  angle,  or  90°,  with 
one  another. 


DOUBLE-RIVETED  JOINTS. 


103 


The  distance  between  the  rivets  in  the  direction  of  the  joint  can  be 
made  42  to  50  per  cent,  greater  than  between  rivets  in  single-riveted 
joints. 

The  diagonal  distance  between  centres  of  rivet  should  be  made 
equal  to  the  distance  in  the  direction  of  the  joints  in  single  riveting. 

Fig.  4. 


Double-riveted  joints  with  punched  holes,  proportioned  according 
to  this  rule,  should  be  40  per  cent,  stronger  than  single-riveted  joints, 
and  with  drilled  holes  about  60  per  cent,  stronger. 

g  84.   Safety  Strength  of  Double-riveted  Lap-joints  with  Punched  Holes 
in  Boiler-shells. 


Steam-pressure, 
Diameter  of  boiler, 
Thickness  of  plate, 
Breaking-strain, 


p  = 


0.35 1 S 
D 

0.35  tS 

P 
Dp 


8- 


0.35  8' 
Dp 


0.35  t 


29 


31 


32 


In  the  following  tables  for  double-riveted  lap-joints,  one  is  headed 
A  for  drilled  holes  and  the  other  B  for  punched  holes,  their  difference 
being  only  in  the  distance  of  rivets.  When  the  boiler-plates  are 
stamped  a  low  figure,  say  45000,  and  the  rivets  are  known  to  be  of 
extra  good  quality,  then  table  B  should  be  used  for  drilled  holes. 

For  boiler-iron  of  high  stamp,  say  65000,  and  the  rivets  of  ordinary 
quality,  then  table  A  should  be  used  for  punched  holes.  The  dimen- 
sions in  the  tables  are  given  to  the  nearest  16ths  of  an  inch. 


104 


STEAM  ENGINEERING. 


TABLE  XXIV. 

A.  Proportions  of  Double-riveted  Lap-joints  with 

Drilled  Holes. 

Thickness 

Rivets. 

Distance  between  Rivets. 

Dist.  between 

Lap  of 

of  plate. 

Diameter. 

Length. 

Central. 

Diagonal. 

Cent,  lines. 

joint. 

t 

d 

I 

d 

1/8 

5/16 

1/2 

1.1/4 

7/8 

5/8 

1.5/8 

3/16 

7/16 

3/4 

1.7/8 

1.5/16 

15/16 

2.3/16 

1/4 

1/2 

1.1/8 

2.1/8 

1.1/2 

1.1/16 

2.9/16 

5/16 

5/8 

1.3/8 

2.5/8 

1.7/8 

1.5/16 

3.1/4 

3/8 

3/4 

1.11/16 

3.3/16 

2.1/4 

1.3/8 

3.7/16 

7/16 

13/16 

1.15/16 

3.3/8 

2.3/8 

1.11/16 

4  inches. 

1/2 

7/8 

2.1/4 

3.9/16 

2.1/2 

1.13/16 

4.1/4 

9/16 

1  inch. 

2.1/2 

3.3/4 

2.5/8 

1.7/8 

4.1/2 

5/8 

1.1/16 

2.13/16 

3.7/8 

2.3/4 

1.15/16 

4.7/16 

11/16 

1.1/8 

3.1/8 

4.1/16 

2.7/8 

2.1/16 

5.1/8 

3/4 

1.3/16 

3.5/8 

4.1/4 

3  inches. 

2.1/8 

5.7/16 

13/16 

1.5/16 

3.11/16 

4.9/16 

3.1/4 

2.5/16 

5.7/8 

7/8 

1.3/8 

3.15/16 

4.15/16 

3.1/2 

2.1/2 

6.7/16 

15/16 

1.1/2 

4.1/4 

5.5/16 

3.3/4 

2.11/16 

6.15/16 

1  inch. 

1.5/8 

4.1/2 

5.5/8 

4  inches. 

2.7/8 

7.1/2 

TABLE  XXV. 

B.  Proportion  of  Double-riveted  Lap-joints  with  Punched 

Holes. 

Thickness 

Rivets. 

Distance  between  Rivets. 

Dist.  between 

Lap  of 

of  plate. 

Diameter. 

Length. 

Central. 

Diagonal. 

Cent,  lines. 

joint. 

t 

d 

I 

d 

1/8 

5/16 

1/2 

1.3/8 

1  inch. 

11/16 

1.7/8 

3/16 

7/16 

3/4 

2  inches. 

1.7/16 

1  inch. 

2.1/8 

1/4 

1/2 

1.1/8 

2.1/4 

1.9/16 

1.1/8 

2.3/8 

5/16 

5/8 

1.3/8 

2.13/16 

2  inches. 

1.7/16 

2.3/4 

3/8 

3/4 

1.11/16 

3.3/8 

2.3/8 

1.11/16 

3.3/8 

7/16 

13/16 

1.15/16 

3.9/16 

2.1/2 

1.13/16 

3.1/4 

1/2 

7/8 

2.1/4 

3.13/16 

2.11/16 

1.15/16 

3.3/4 

9/16 

1  inch. 

2.1/2 

4  inches. 

2.13/16 

2  inches. 

4.1/4 

5/8 

1.1/16 

2.13/16 

4.1/8 

2.15/16 

2.1/16 

4.3/4 

11/16 

1.1/8 

3.1/8 

4.5/16 

3.1/16 

2.3/16 

5.1/8 

3/4 

1.3/16 

3.5/8 

4.1/2 

3.3/16 

2.1/4 

5.3/8 

13/16 

1.5/16 

3.11/16 

4.7/8 

3.7/16 

2.7/16 

5.5/8 

7/8 

1.3/8 

3.15/16 

5.1/4 

3.11/16 

2.5/8 

6.1/8 

15/16 

1.1/2 

4.1/4 

5.5/8 

3.15/16 

2.9/16 

6.5/8 

1  inch. 

1.5/8 

4.1/2 

6  inches. 

4.3/16 

3  inches. 

7  inches. 

STRENGTH  OF  LAP-JOINTS. 


105 


§  85.  Safety  Strength  of 

Double-riveted  Lap-joints  with 
in  Boiler-shells. 

Drilled  Holes 

Steam-pressure 

0.4  tS 

33 

Diameter  of  boiler 

P        D 
D_OAtS  ^ 

34 

P 

OK 

'    QAS    ' 

oo 

s   Dp 

oo 

8    0.4  <     •        '        '        ' 

Example  33.  What  pressure  can  be  carried  with  safety  in  a  boiler  of 
D  =  72  inches  diameter,  made  of  steel  plates  stamped  S=  75000  pounds 
tensile  strength  and  t  =  %  inch  thick,  when  the  boiler  is  double-riveted 
with  drilled  holes? 

0.4x0.5x75000     ( 
p  =  —   — — —   —  =  208  pounds  to  the  square  inch. 

TABLE  XXVI. 
\  86.  Coefficients  X  for  Safety  Strength  of  Lap-joints. 


Construction  of  Shell. 

X 

Per  cent, 
of  strength. 

05 

100 

04 

80 

035 

70 

Single-riveted  drilled  holes  

0.3 

60 

0  25 

50 

Steam-pressure, 


P  = 


XtS 
D 


Diameter  of  boiler,         D  = 


Thickness  of  plate, 


37 
38 
39 


Breaking-strain, 


40 


106  STEAM  ENGINEERING. 

§  87.  The  greatest  strain  in  a  cylindrical  boiler-shell  is  in  the  direc- 
tion of  the  circumference,  for  which  the  double-riveted  joints  are  first 
required  in  the  direction  of  the  length  of  the  boiler. 

Longitudinal  strain,         =TcDtS=p-Dt        ...        41 

Required  thickness  of  metal,         t  =  — -  ...        42 

Transverse  strain,  =  t  S  =  p  D         .        .        43 

Required  thickness  of  metal,         t  =  *—-          ...        44 


That  is  to  say,  the  longitudinal  strain  is  only  one-half  of  the  trans- 
verse strain,  or  that  single-riveted  joints  with  punched  holes  around 
the  boiler  are  stronger  than  double-riveted  joints  with  drilled  holes 
longitudinally. 

Double-riveted  joints  are  therefore  required  only  longitudinally. 

STRENGTH   OF   FLUES   AND   TUBES   FOR   EXTERNAL   PRESSURE 
TO   COLLAPSE. 

§  88.  The  most  reliable  experiments  on  this  subject  yet  made  are 
those  of  the  late  Mr.  Fairbairn,  who  stated  that  the  strength  of  the 
flue  is  inversely  as  its  length,  but  he  proposed  different  coefficients  for 
different  lengths. 

By  analyzing  closely  the  results  of  Mr.  Fairbairn's  experiments  and 
by  using  constant  coefficients,  we  find  that  the  strength  is  inversely  as 
the  square  root  of  the  length  of  the  flue  or  tube. 

The  following  formulas  are  deduced  from  the  results  of  those  ex- 
periments without  regard  to  the  formulas  proposed  by  Mr.  Fairbairn. 

D  =  diameter  of  the  flue  or  tube  in  inches. 
L  =  length  of  the  same  in  feet. 

t  =  thickness  in  fractions  of  an  inch  of  the  iron  in  the  flue. 
p  =  steam  pressure  in  pounds  per  square  inch. 
S= tensile  strength  per  square  inch  of  iron  in  the  flues. 


COLLAPSING  FLUES.  107 


89.   Collapsing  Strength  of  Flues  subjected  to  External  Pressure. 

4  Si2 
Steam-pressure,  p  =  —    — .      .  .        .       .        .41 

DyL 

4  a  ft 

Diameter  of  flue,         D  = - 42 

Pl/L 


Thickness  of  metal,        t  =  \.  .         .         .43 

(4.  K  /2  \2 
-) 44 
PD  I 

Assuming  one-fourth  of  the  collapsing  strength  as  safety  for  the 
flue,  the  formulas  will  simply  dispense  with  the  coefficient  4. 


90.  Safety  Strength  of  Flues  and   Tubes  from  Collapsing  by  External 
Pressure. 

S  t? 
Steam-pressure,  p  =  —  -  —  .          .        .        .        .45 


Diameter  of  flue,         D  =  —  l—  .....     46 
Pl/L 


Thickness  of  iron,          <  =  ^^^-^.          ...     47 

Length  of  flue,  L==(~^l         '        '        '        '    48 

Example  4.5.  A  flue  made  of  iron  $=50000  pounds  strength  is 
D  =  18  inches  in  diameter  and  L  =  16  feet  long,  by  i  =  f  of  an  inch 
metal.  Required  what  steam-pressure  the  flue  can  stand  with  safety  ? 

50000  x  32 
p  =  —  —  =  97.66  pounds  to  the  square  inch. 

isxj/iexs2 


108  STEAM  ENGINEERING. 

STAYING    OF   FLAT   BOILER   SURFACES. 

§  91.  Flat  surfaces  subject  to  steam-pressure  in  boilers  must  be 
stayed  in  order  to  keep  their  proper  flat  position  as  intended,  and 
thus  the  whole  steam-pressure  on  such  surface  must  be  borne  by  stays. 

A  =  area  in  square  inches  to  be  stayed,  a  =  section  area  of  each 
stay  in  square  inches,  n  =  number  of  stays  required,  p  =  steam- 
pressure  in  pounds  per  square  inch.  S  =  tensile  strength  of  the  iron 
in  the  stays.  D  =  distance  between  the  stays  in  inches. 


Ap    ..  IPressureon) 
Ap-an8      and      a--^.  44  [ 


nS 

Number  of  stays,        n  =  — -.  45 
aS 


each  stay, 


_ 
48 


Distance,          D  =     —  .  47 

\  p 


Suppose  the  stays  to  be  round  of  diameter  d  ;  then  a  -=  - 


48 


Allowing  28  per  cent,  for  safety  of  the  ultimate  strength  of  stays, 
we  have 

Safety  Formulas  for  Stay-bolts. 


Diameter  of  stay,  d  =  4  Z)-*  /-.  49 
*  S 

Distance  apart,     D  -  --J-.    .  50 
4\» 

a*                                    d  * 
Steam-pressure,    p  =  -.    . 

Iron  required,       S=*  _£, 

51 
52 

Example  50.  The  iron  for  stay-bolts  in  a  steam-boiler  is  d  =  1  inch 
diameter  and  S  =  62500  pounds  strength,  to  be  used  in  a  pressure  of 
p  =  64  pounds  to  the  square  inch.  Required  the  distance  apart  of 
the  stays? 

1    162500 


The  strength  of  all  the  connections  of  the  stays  must  be  equal  to 
that  of  the  solid  stay.  When  the  sections  of  the  stays  are  square  or 
rectangular,  the  area  must  be  equal  to  that  corresponding  to  the 
diameter  d  of  the  round  iron. 

The  following  table  is  calculated  for  stays  of  one  inch  diameter  ;  but 
when  the  stays  are  more  or  less,  the  spaces  between  them  should  be 
that  much  more  or  less;  for  instance,  if  the  stays  are  f  inch  diameter, 
the  spaces  in  the  table  should  be  multiplied  by  f  ,  and  so  on. 


STRENGTH  OF  RIVETED  JOINTS. 


109 


TABLE  XXVII. 

Distance  in  Inches  between  Boiler-stays  One  Inch  in 
Diameter. 

Steam 
pressure. 

45,000. 

Breaking  str 
50,000. 

iin  in  pound 
55,000. 

s  per  square 
60,000. 

nch  of  stay. 
65,000. 

70,000. 

P- 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

Inches. 

25 

10.6 

11.2 

11.7 

12.5 

12.7 

13.2 

30 

9.68 

10.2 

10.7 

11.4 

11.6 

12. 

35 

8.96 

9.45 

9.9 

10.5 

10.8 

11.1 

40 

8.38 

8.84 

9.26 

9.84 

10.1 

10.4 

45 

7.9 

8.34 

8.74 

9.28 

9.51 

9.84 

50 

7.5      . 

7.9 

8.28 

8.8 

9.02 

9.34 

'     55 

7.15 

7.54 

7.9 

8.4 

8.6 

8.9 

60 

6.85 

7.22 

7.56 

8.04 

8.24 

8.52 

65 

6.58 

6.94 

7.26 

7.72 

7.91 

8.18 

70 

6.34 

6.68 

6.99 

7.43 

7.62 

7.88 

75 

6.12 

6.45 

6.75 

7.18 

7.36 

7.61 

80 

5.93 

6.25 

6.54 

6.96 

7.12 

7.38 

85 

5.75 

6.07 

6.35 

6.75 

6.91 

7.15 

90 

5.59 

5.89 

6.17 

6.56 

6.72 

6.96 

95 

5.43 

5.73 

6. 

6.39 

6.54 

6.77 

100 

5.3 

5.6 

5.86 

6.23 

6.37 

6.6 

110 

5.05 

5.32 

5.58 

5.93 

6.08 

6.29 

120 

4.84 

5.1 

5.35 

5.68 

5.82 

6.02 

130 

4.56 

4.9 

5.13 

5.46 

5.58 

5.79 

140 

4.48 

4.73 

4.95 

5.26 

5.38 

5.58 

150 

4.33 

4.56 

4.78 

5.08 

5.2 

5.39 

160 

4.19 

4.42 

4.62 

4.92 

5.03 

5.21 

170 

4.06 

4.29 

4.49 

4.78 

4.88 

5.06 

180 

3.95 

4.17 

4.36 

4.64 

4.75 

4.91 

190 

3.85 

4.06 

4.25 

4.52 

4.63 

4.79 

200 

3.74 

3.95 

4.14 

4.4 

4.51 

4.66 

210 

3.66 

3.86 

4.04 

4.3 

4.4 

4.56 

220 

3.57 

3.77 

3.94 

4.2 

4.3 

4.44 

230 

3.5 

3.68 

3.86 

4.1 

4.2 

4.35 

240 

3.42 

3.61 

3.78 

4.02 

4.11 

4.26 

250 

3.35 

3.53 

3.7 

3.93 

4.03 

4.17 

260 

3.29 

3.47 

3.63 

3.86 

3.95 

4.1 

270 

3.23 

3.4 

3.56 

3.79 

3.88 

4.02 

280 

3.16 

3.34 

3.5 

3.71 

3.8 

3.94 

290 

3.11 

3.28 

3.43 

3.65 

3.74 

3.87 

300 

3.06 

3.23 

3.38 

3.6 

3.68 

3.81 

110  STEAM  ENGINEERING. 


STEAM-POWER  WITHOUT  FIRE. 

§  92.  When  water  is  heated  under  high-pres- 
Fig- 6>  sure  in  a  closed  vessel,  the  work  so  stored  can  be 

utilized  for  motive-power  after  the  fire  is  with- 
drawn. 

Fig.  5  represents  a  section  of  a  cylindrical  ves- 
sel nearly  full  of  hot  water,  above  which  surface 
steam  is  to  be  conducted  to  a  motor  through  the 
valve  and  pipe  a. 

Suppose  no  heat  to  radiate  from  the  vessel  and 
no  discharge  of  steam,  there  will  then  only  be  a 
static  pressure  corresponding  to  the  temperature 
of  the  water,  and  no  work  is  performed. 

The  combination  of  heat,  water  and  steam  enclosed  in  a  vessel  con- 
stantly tends  to  keep  the  presence  and  temperature  in  equilibrium — 
that  is,  a  given  pressure  corresponds  with  a  certain  temperature. 
Therefore,  if  steam  is  allowed  to  escape  through  the  pipe  a,  the  tem- 
perature and  pressure  in  the  steam-room  will  be  lowered  below  that 
in  the  water,  the  result  of  which  is  that  the  excess  of  temperature  in 
the  water  will  generate  more  steam  to  establish  equilibrium. 
W=  pounds  of  water  in  the  vessel. 
T  =  temperature  Fahr.  of  the  steam  and  water. 
P=  steam-pressure  in  pounds  per  square  inch  above  vacuum  in  the 


C=  cubic  feet  of  steam  used  per  double  stroke  in  a  steam-engine. 

n  =  double  strokes  per  minute  of  the  steam  piston. 

p  «=  steam-pressure  in  pounds  per  square  inch  above  that  of  the  at- 
mosphere in  the  cylinder. 

H=  units  of  heat  per  pound   in  the  water   before  the  engine  is 

started. 

H'  =  units  of  heat  per  pound  of  the  water  in  the  vessel  after  the  en- 
gine has  made  n  revolutions. 

h  =  units  of  heat  per  cubic  foot  of  the  steam  driving  the  engine. 

w  =  pounds  of  water  passed  through  the  engine  in  form  of  steam. 

^  =  weight  per  cubic  foot  of  steam. 

§  93.  The  primitive  number  of  units  of  heat  in  the  vessel  is  W  H, 
and  after  the  engine  has  made  n  revolutions,  that  heat  will  be  reduced  to 

H'(W-in)=  WH-Cnh.   .        .        .        1 
The  heat  consumed  by  the  engine  will  then  be  C  n  h. 


STEAM  WITHOUT  FIRE.  Ill 

The  weight  w  of  steam  passed  through  the  engine  is  w  =  (7^  n,  which, 
inserted  for  w  in  Formula  1,  gives 

H'(W-C^  n)=WH-Cnh.        .        .        2 
Revolutions,  »--E2..  .        3 


Example  3.  A  vessel  containing  200  cubic  feet  of  water  of  temper- 
ature T=358°,  corresponding  to  a  pressure  of  P=  150  pounds  to  the 
square  inch,  supplies  steam  which  is  wire-drawn  to  a  pressure  of  p  =  30 
pounds  to  an  engine  using  (7=1.5  cubic  feet  of  steam  for  each  revolu- 
tion. 

Required  how  many  revolutions  the  engine  will  make  before  the 
steam-pressure  in  the  vessel  is  reduced  to  p  =  30  or  P==  45  pounds  ? 

The  weight  of  water  itf  the  boiler  is 

W=  200  x  56.073  =  11214.6  pounds. 

H=  330.75.    H'=  241.32.    f  =  0.11111.    A  =  129.51. 

See  tables  Nystrom's  Pocket-Book  for  these  data. 

11214.6(330.75-241.32) 

Revolutions,          n  =  —  —  =  6570.6. 

1.5(129.51-0.1111x241.32) 

The  water,  evaporated  to  steam,  will  be 

w  -  1.5  x  0.11111  x  6570.6  =  1095.1  pounds, 

or  nearly  10  per  cent,  of  the  primitive  water  in  the  vessel. 

Assuming  the  engine  to  make  80  revolutions  per  minute,  it  will  run 

—  -j-  =  1.369  hours,  with  the  steam  generated  in  the  vessel. 
80  x  60 

Practically,  the  radiation  of  heat  from  the  vessel  and  steam-pipe  will 
reduce  this  time  perhaps  15  cents. 

Dr.  Emile  Lamm  of  New  Orleans  constructed  a  locomotive  upon 
the  above  principle  with  heated  water  without  fire,  and  which  was 
used  on  General  Beauregard's  road  in  the  year  1872. 


112  STEAM  ENGINEERING. 


PERMANENT  GASES. 

§  94.  Permanent  gases,  in  distinction  from  vapors,  are  those  that 
cannot  be  condensed  to  liquid  under  ordinary  temperatures  and 
pressures. 

Oxygen,  nitrogen  and  hydrogen  are  the  principal  permanent  gases, 
and  any  mechanical  mixture  of  either  two  or  all  the  three  will  remain 
a  permanent  gas  like  atmospheric  air,  which  is  a  mixture  of  oxygen 
and  nitrogen ;  but  any  chemical  combination  of  either  two  or  all  the 
three  becomes  a  vapor  which  is  condensable  to  liquid  like  that  of 
oxygen  and  hydrogen,  forming  steam,  which  condenses  to  water  under 
temperature  212°  Fahf.  and  freezes  solid  at  32°. 


ELASTICITY   OF   PERMANENT   GASES. 

§  95.  Permanent  gases  are  perfectly  elastic — that  is,  the  product 
of  volume  and  pressure  of  a  definite  weight  of  gas  will  remain  con- 
stant under  constant  temperature.  For  instance,  if  the  volume  is 
compressed  to  one-half,  the  pressure  will  be  double;  and  if  again  ex- 
panded to  its  primitive  volume,  the  original  pressure  will  be  restored 
if  the  temperature  remains  constant.  When  the  temperature  varies, 
the  product  of  volume  and  pressure  will  also  vary  in  a  direct  ratio  to 
the  difference  of  temperature. 

Call  ^  and  P  volume  and  pressure  of  a  definite  weight  of  gas  of 
temperature  T.  V  and  p  =  volume  and  pressure  of  the  same  gas,  but 
of  temperature  t.  P  and  p  mean  the  actual  pressures  of  the  gas 
above  vacuum. 

Then         i*-1+-*--«.  ! 


That  is  to  say,  the  ratio  of  the  products  of  volume  and  pressure  in- 
creases arithmetically  as  the  difference  of  temperature. 

The  experiments  on  elasticity  of  permanent  gases  made  by  Regnault 
and  Rudberg  show  that  c  is  constant  for  any  difference  of  temper- 
ature within  the  limit  of  those  experiments. 

Call  Vp  =  1  when  t  =  32°,  and  find  the  value  of  ^  Pwhen  T  -  212° 
or  a  difference  in  temperature  of  180°.  Under  this  condition  the  ex- 
periments of  Regnault  and  Rudberg  show  that 


PERMANENT  OASES.  113 


,  that  is,  1+0.365.       .        .        2 


Vp 


Consequently,    0.365  =  -^-=-^  =  —,  3 

c  c 


of  which  c  =  —  —  =  493.15. 

0.365 

\^  _P  T—  t 

Then  —  =  1  +  —      —  for  all  permanent  gases.       4 

vp  493.15 

Drop  the  fraction  0.15,  and  say  493. 
Assume  the  pressure  to  be  constant — 

'     That  is,  —  =  1 5 

* 

Then  -?  - 1  +     ...    .  6 


Call  V  «=  1  at  the  temperature  t  =  32°.  Then  the  volume  if  can  be 
determined  by  Formula  7  for  any  other  temperature  T,  and  under 
constant  pressure.  For  instance,  suppose  the  temperature  of  the  vol- 
ume #to  be  reduced  to  T°  =  -461°,  then 


the  volume      =  461  ~8 


2\= 


This  implies  not  only  that  the  volume  of  a  permanent  gas  can  be 
reduced  to  nothing,  and  even  negative,  but  that  matter  which  exists 
in  the  universe  may  be  rendered  extinct  or  less  than  nothing,  which 
is  simply  preposterous.  Therefore  c  cannot  be  a  constant  quantity. 

It  is  generally  supposed  by  scientific  men  of  our  days  that  the  tem- 
perature 461°  below  Fahrenheit's  zero  is  an  absolute  zero  or  lowest 
limit  of  temperature,  which  hypothesis  is  based  upon  the  assumption 
that  for  all  permanent  gases 


p  V  493 

This  formula  implies  that  the  intervals  between  the  temperatures 

8 


114  STEAM  ENGINEERING. 

progress  in  the  same  ratio  as  do  the  intervals  between  P  -fi  :  p  V, 
which  the  author  inclines  to  doubt. 

§  96.  We  have  yet  no  experimental  data  and  not  sufficient  knowledge 
on  the  subject  by  which  to  contradict  the  existence  of  this  absolute  zero 
at  that  place.  It  is  evident,  however,  that  matter  cannot  be  rendered 
extinct,  but  that  there  must  exist  some  low  temperature  at  which  the 
force  of  expansion  of  the  heat  is  equal  to  or  less  than  the  force  of 
attraction  between  the  atoms  composing  the  gas,  which  must  then  be  a 
liquid,  solid  or  powder  of  a  definite  volume ;  and  it  is  reasonable  to 
suppose  that  the  temperature  of  that  volume  can  be  further  reduced. 

Considering  that  water  is  practically  incompressible,  we  may  assume 
that  the  atoms  of  oxygen  and  hydrogen  are  there  in  close  contact,  and 
represent  the  volume  of  these  gases  in  a  liquid  or  solid  state. 

One  cubic  foot  of  water  at  32°  weighs  62.4  pounds,  of  which  there 
are — 

54.6  pounds  of  liquid  oxygen  in  ^  cubic  foot. 
7.8  pounds  of  liquid  hydrogen  in  f  "       " 
1  pound  liquid  oxygen     =0.006105  cubic  foot. 
1  pound  liquid  hydrogen  =  0.08547        "        " 
1  pound  oxygen  gas  at  32°  =  11.28         "        " 
1  pound  hydrogen  gas  at  32°  =  180        "        " 

11.28 

1  volume  liquid  oxygen  = : =  1847.7  volumes  of  oxygen 

0.006105 
gas  at  32°. 

1  volume  liquid  hydrogen  = —  =  2106  volumes  of  hydro- 
gen gas  at  32°. 

1  volume  oxygen  gas  =  0.0005412  volumes  of  liquid  oxygen. 
1  volume  of  hydrogen  gas  =  0.0004748  volumes  of  liquid  hy- 
drogen. 

Allowing  for  contraction  of  the  liquid  volume  by  cooling  from  32° 
to  -461°  or  !F-t  =  493°,  at  the  same  rate  as  ice  contracts,  about 
0.8547  of  that  at  32°. 

Volume  of  liquid  oxygen  at  -461°  is  then 

0.000541 2  x  0.8547  #=  0.00046256  V. 
Volume  of  liquid  hydrogen  at  -461°  is 

0.0004748  x  0.8547  #  =  0.00040581  V. 


PERMANENT  OASES.  115 

This  should  be  the  ultimate  volumes  to  which  gases  of  oxygen  and 
hydrogen  can  be  reduced  by  cooling  from  +32°  to  -461°. 

The  oxygen  and  hydrogen  of  one  cubic  foot  of  water,  dissolved  into 
their  respective  gases,  would  occupy  1919.9  cubic  feet  at  32°  Fahr., 
or  2610.66  cubic  feet  at  212°,  and  under  atmospheric  pressure. 

§  97.  It  is  supposed  in  the  preceding  calculation  that  if  one  cubic 
foot  of  water  is  resolved  into  its  elements  and  still  remain  in  liquid 
form,  the  hydrogen  would  occupy  %  and  the  oxygen  ^  of  the  cubic 
foot ;  but  such  would,  however,  not  be  the  case.  The  hydrogen  would 
occupy  the  whole  cubic  foot,  whether  the  oxygen  is  in  it  or  not.  The 
atoms  of  hydrogen  may  be  represented  by  large  potatoes  filling  a 
bushel,  but  the  real  capacity  of  the  potatoes  is  only  ^  of  that  bushel ; 
the  other  ^  can  be  filled  up  with  buckshot,  representing  the  atoms  of 
oxygen.  The  potatoes  would  occupy  the  same  space  whether  the  shot 
are  there  or  not.  Such  is  the  case  with  hydrogen  and  oxygen  in 
water ;  but  when  these  elements  are  resolved  into  their  respective 
gases,  they  will  occupy  50  per  cent,  more  volume  than  when  chem- 
ically combined  in  the  form  of  vapor.  The  result  of  the  preceding 
calculation  is,  however,  correct. 

It  is  reasonable  to  suppose  that  the  so-called  permanent  gases  be- 
come vapors  and  finally  condense  to  liquids  and  freeze  to  solids  at 
a  low  temperature,  which  we  have  not  yet  been  able  to  produce,  and 
that  there  is  therefore  a  limit  beyond  which  the  volume  of  those  gases 
cannot  be  reduced.  The  pressure,  on  the  other  hand,  is  reduced  to 
nothing  at  a  low  temperature  when  the  vapors  condense  to  liquid  and 
freeze  to  ice ;  but  that  is  no  proof  of  an  absolute  zero  having  been 
reached  beyond  which  there  exists  no  temperature. 

Steam  highly  superheated  behaves  very  much  like  permanent  gases; 
and  if  experimented  upon  without  knowing  the  lower  temperatures  at 
which  it  condenses  to  water  and  freezes  to  ice,  the  inference  might  be 
that  there  exists  an  absolute  zero  at  which  the  pressure  and  volume 
of  steam  become  nothing,  and  beyond  which  there  exists  no  temper- 
ature. 

Carbonic  acid  gas  under  ordinary  pressures  and  temperatures  be- 
haves like  permanent  gases  ;  but  at  low  temperatures  and  high  pres- 
sures it  becomes  a  vapor  which  can  be  condensed  to  liquid  and  even 
frozen  solid. 

Water  and  ice  evaporate  under  low  temperatures,  as  shown  by  the 
experiments  of  Regnault  and  Dalton.  A  wet  cloth  exposed  to  very 
cold  weather  freezes  stiff,  but  finally  the  ice  in  it  evaporates  and 
leaves  the  cloth  dry. 

The  formulas  which  the  writer  has  deduced  from  the  experiments 


116  STEAM  ENGINEERING. 

of  Regnault  and  Dalton,  indicate  that  the  pressure  of  aqueous  vapor 
is  reduced  to  nothing  at  the  temperature  - 101°  below  Fahr.  zero. 

Such  is  most  likely  the  case  with  all  permanent  gases — namely,  that 
at  some  low  temperature  different  for  each  kind  of  gas  the  pressure  is 
reduced  to  nothing,  whilst  the  volume  remains  definite,  whether  in  the 
form  of  gas,  vapor,  liquid  or  solid.  Therefore,  when  the  matter  is  in 
the  form  of  a  gas  or  vapor  at  the  low  temperature  where  the  pressure 
is  reduced  to  nothing,  the  force  of  attraction  between  its  atoms  is  equal 
to  the  force  of  expansion  by  heat,  and  the  gas  occupies  a  definite 
volume  like  a  cloud  in  the  air.  Thus,  the  top  of  our  atmosphere 
would  maintain  a  smooth  surface  like  the  ocean,  omitting  the  disturb- 
ance caused  by  change  of  temperature  and  currents  of  wind  below. 

§  98.  Within  the  limit  of  our  practice  we  can  safely  use  the  for- 
mula 

Pf          T-t 
pV  493  ' 

Under  constant  pressure  the  increase  of  volume  of  any  permanent 
gas,  per  degree  of  increased  temperature — that  is,  when  T-t  =  l  will 
be  ,|y- 0.0020284. 

For  simplicity  in  elucidating  the  subject  and  for  the  formation  of 
tables,  it  is  best  to  assume  a  standard  temperature,  t  =  32°  Fahr.,  at 
which  all  other  quantities  are  compared. 


493        pV 

The  value  of  x  is  calculated  for  every  degree  of  temperature  from 
0°  to  500°,  for  every  10°  from  500°  to  1200°,  and  for  every  100° 
from  1200°  to  2300°,  in  Table  XXX. 

\  99.  Variable  Volume  under  Constant  Pressure. 
Temperature,  z  =  — 1 

Heated  volume,         ^  =  Vx 2 

Cold  volume,  %T=  — 3 


Example  1.  A  volume  %f=36  cubic  feet  of  air  is  to  be  heated  from 
32°  until  the  volume  is  expanded  to  "^  =  48  cubic  feet.  Required 
the  temperature  of  the  expanded  volume  ? 


PERMANENT  OASES.  117 


48 


Find  1.5  in  column  x  in  the  table,  which  corresponds  to  the  re- 
quired temperature,  T  =  279  Fahr. 

If  the  volume  V  had  been  heated  from  a  higher  temperature,  say 
t  =  60°,  then  60-32  =  28  and  279  +  28  =  307°,  the  required  temper- 
ature. 

Example  2.  A  volume  of  air  %P=24  cubic  feet  is  heated  from  t  = 
48°  to  T=  450°.  Required  the  volume  ^  ? 

In  this  case  48-32  =  16  and  450  +  16=466°.  Find  x  for  466°, 
which  in  the  table  corresponds  to  x  =  1.88. 

Volume  ^  =  24  x  1.88  -  45.12  cubic  feet. 

'Example  3.  A  volume  of  air  V  =  148  cubic  feet,  and  of  tempera- 
ture T=250°,  is  to  be  cooled  down  to  £  =  32°.  What  will  be  the 
volume  of  the  cooled  air? 

140 
Cold  volume,         #=  -         =  102.63  cubic  feet. 


\  100.  Variable  Pressure  under  Constant  Volume. 

p 

Temperature,  x  =  — 4 

P 

High  pressure,         P=px 5 

p 
Low  pressure,  p  =  — 6 

Example  4-  A  volume  of  permanent  gas  enclosed  in  a  vessel  exerts 
a  pressure  of  jt>  =  15  pounds  to  the  square  inch,  and  is  €  =  32°  in 
temperature.  To  what  temperature  must  that  gas  be  elevated  in 
order  to  increase  the  pressure  to  P=25  pounds  to  the  square  inch? 

or 

x  =      =  1.6666. 
15 

The  required  temperature  is  T=361°. 

Had  the  primitive  temperature  in  the  vessel  been  more  or  less  than 
32°,  the  required  temperature  would  have  been  that  much  more  or 
less. 

Example  5.   A  gas  of  temperature   £  =  21°,  enclosed  in  a  vessel 


118  STEAM  ENGINEERING. 

under  a  pressure  of  p  =  12  pounds  to  the  square  inch,  is  to  be  heated 
to  a  temperature  T=  180°.  Required  the  pressure  of  the  heated  gas? 

In  this  case  T- 180  +  11  =191°. 

Pressure  P=  12  x  1.3224  =  15.8888  pounds  per  square  inch. 

Example  6.  The  temperature  of  a  permanent  gas  enclosed  in  a  vessel 
is  !F=120°,  and  pressure  P=20  pounds  to  the  square  inch,  is  to  be 
reduced  to  t  =  5°.  Required  the  pressure  p  of  the  cold  gas  ? 

In  this  case  T=  120  +  5  +  32  =  157,  and  x  -  1.2535. 

20 

Pressure,       p  = —  =  15.95  pounds  per  square  inch. 

1.2535 

2  101.  VOLUME   AND   PRESSURE   BOTH  VARIABLE. 
Temperature,  x  =  — 7 

T)    *fy 

High  pressure,  P  =  ±_^ — 8 

Low  pressure,  p  =  — — 9 

Warm  volume,  ^  =  *—- —  .        .        .        .        .10 

Cold  volume,  W= —    •  .        .        .        .       11 

px 

Example  7.  A  volume  of  air  %f=16  cubic  feet,  pressure  p  =  15 
pounds  to  the  square  inch  and  temperature  323,  is  to  be  heated  until 
the  volume  becomes  ^  =  24  cubic  feet  and  pressure  P=  20  pounds  to 
the  square  inch.  Required  the  temperature  of  the  heated  air. 


16x15 
The  required  temperature  is  T=  530°. 

Example  8.  A  volume  of  air  ^  =  42  cubic  feet  and  temperature 
T=480°  has  been  expanded  from  3^=28  cubic  feet  of  temperature 
t  =  62°  and  pressure  p  =  15  pounds.  Required  the  pressure  of  the 
expanded  volume? 

62  -  32  =  30°,  and  480  -  30  =  450.    x  =  1 .8477. 

,    15x28x1.8477 
Pressure,  P=  — =  18.4Y  7  pounds. 


IE  IR,  JR, 


PAGE 

LINE  FROM 

FOR 

READ 

TOP 

BOTTOM 

3§ 



6 

6.4 

6.88 

40 

i5 



3.62 

2.62 

40 

16 



3^7 

2.67 

55 

5 



acid. 

oxide. 

69 

4 



^f~ 

VW 

i 

P 

131 

H 

*\r 

v~ 

137 
1  68  . 

— 

2 

8 

1421700 
491.6° 

14217000 
391.6° 

PERMANENT  OASES. 


119 


Example  9.  The  temperature  of  a  permanent  gas  is  T=248°,  pres- 
sure P=48  pounds  and  volume  ^r  =  96  cubic  feet.  The  volume  is  to 
be  reduced  to  V=72  cubic  feet  of  temperature  t  =  72°.  Required 
the  pressure  p  ? 

72-32  =  40°.    248° -40°  =  208°.    x  =  1.3569. 


Pressure, 


48 


72x1.3569 


-  =  47  pounds. 


SPECIFIC    HEAT    OF   PERMANENT   GASES. 

§  102.  The  specific  heat  of  a  gas  is  that  fraction  of  a  unit  of  heat 
required  to  elevate  the  temperature  of  one  pound  of  that  gas  one  de- 
gree Fahrenheit.  It  is  constant  under  constant  pressure,  but  under 
variable  pressure  the  specific  heat  is  inversely  as  the  square  root  of 
the  pressure. 

TABLE  XXVIII. 
Specific  Heat  under  Constant  Pressure  and  Temperature  32°. 


Kinds  of  gases. 

Pounds  per 
cubic  foot. 

Cubic  foot 
per  pound. 

Specific 
Water  =  1. 

gravity. 
Air  =  1. 

Specific 
heat. 

Atmospheric  air  

f 

0.08042 
0.08888 
0.07837 
0.00559 
0.07837 
0.12333 
0.05021 

G 

12.433 
11.251 
12.760 
178.84 
12.760 
8.108 
19.915 

0.00130 
0.00143 
0.00126 
0.00009 
0.00126 
0.00197 
0.00634 

1.000 
1.104 

0.972 
0.069 
0.972 
1.527 

0.488 

8 

0.25 
0.23 
0.275 
3.3 
0.288 
0.221 
0.475 

Oxygen  gas  

Nitrogen  gas  

Hydrogen  gas  

Carbonic  oxide. 

Steam 

S  =  specific  heat  under  constant  pressure,  as  in  the  table  above. 
s  =  mean  specific  heat  under  any  pressure  and  volume  from  32° 

to  T. 
^>  =  14.7  pounds  to  the  square  inch  pressure  of  the  gas  at  £  =  32° 

Fahr. 

P  =  pressure  of  the  same  gas  at  the  temperature  T. 
%T=  volume  in  cubic  feet  of  the  gas  at  32°. 

ifr  =  volume  of  the  same  gas,  but  of  pressure  P  and  temperature  T. 
W=  weight  in  pounds  of  the  gas  experimented  upon. 
*$  =  weight  in  a  fraction  of  a  pound  per  cubic  foot  of  the  gas. 
h  =  units  of  heat  in  W  pounds  of  gas  elevated  from  32°  to  T,  or 

from  a  pressure  of  14.7  to  P  pound. 


120  STEAM  ENGINEERING. 


\  103.  Formulas  for  Heat  in  Gases  in  regard  to  Pressure. 
Mean  specific  heat,  s  =  S  \l— 1 


Units  of  heat,  h  =  S  Jf\/^-r(23-32°).    .         .        .     2 

Temperature,  T=  — 

Pressure  of  gas,  P=p  | 

Example  1.  What  is  the  mean  specific  heat  of  air,  heated  under 
constant  volume  from  a  pressure  ^  =  14.7  to  P=26  pounds  to  the 
square  inch  ? 

Mean  specific  heat,        s  =  0.25^^  =  0.188. 

Example  2.  How  many  units  of  heat  are  there  in  W=  8  pounds  of 
carbonic  acid,  heated  from  32°  to  T=450°,  and  from  a  pressure  14.7 
to  P=20  pounds  per  square  inch? 

Units  of  heat,        h  =  0.221  x  8-^^(450  -  32)  =  629.25. 

Example  3.  What  will  be  the  temperature  of  W=  12  pounds  of  air 
supplied  with  h  =  864  units  of  heat,  which  increases  the  pressure  from 
p  =  14.7  to  P=  24  pounds  to  the  square  inch  ? 


Temperature,         r-^  32  =  323.33. 

Example  4-  What  pressure  will  be  attained  by  heating  W=  24 
pounds  of  carbonic  oxide  from  32°  to  T=280°,  with  A  =  2400  units 
of  heat  supplied  to  the  gas  in  a  closed  vessel  ? 


Pressureof  gas,      P-14.7  =  8.8513. 


In  this  case  the  pressure  became  less  than  the  primitive  pressure, 
the  reason  of  which  is  that  the  volume  was  expanded  in  order  to  ad- 
mit 2400  units  of  heat  without  increasing  the  temperatures  over  280°. 


HEAT  IN  PERMANENT  OASES.  121 

|  104.  Formulas  for  Heat  in  Gases  in  regard  to  Volume. 

Mean  specific  heat,  s  =  &\-jj- 5 

Units  of  heat,  h  =  S  fJ2-?C  T-  32).  ...     6 

Temperature,  T= — ±p\/~] —  +  32.        .        .         .7 

Volume,  ^^aTl"  r  *         '        *     ^ 

Example  5.    Required   the   mean   specific   heat   of  hydrogen   gas, 
heated  from  32°  to-T=450°,  and  the  volume  increased  50  per  cent.? 

a;  =  1.8477. 


Specific  heat,         s  =  3.3  -J  —  —  -  =  2.9733. 
»  .L  x  1,04  /  / 

Example  6.  How  many  units  of  heat  are  required  to  heat  ^=36 
cubic  feet  of  nitrogen  gas  from  32°  to  T=400°,  and  expand  the 
volume  to  ^  =  40  cubic  feet  ? 

Units  of  heat,      h  =  0.275  x  0.07837  J^6  *  ,4°(400  -  32)  =  227.75. 

»  1  .  i  4uo 

By  the  aid  of  the  following  table  the  preceding  formulas  and  calcu- 
lations can  be  much  simplified  by  calling 


The  value  of  y  is  calculated  for  different  temperatures  in  the  table, 
by  the  aid  of  which  the  units  of  heat  in  any  gas  can  be  found  by  the 
following  formulas. 


y  = 


.    10 
.    11 

13 


122  STEAM  ENGINEERING. 

Having  giveii  the  weight  W,  volumes  ^  and  #,  and  the  units  of 
heat  h,  in  any  permanent  gas,  calculate  the  value  ofy  by  Formula  12- 
or  13,  which  gives  the  corresponding  temperature  of  the  gas  in  the 
table. 

Example  11.  How  many  units  of  heat  are  required  to  elevate  the 
temperature  of  #=160  cubic  feet  of  air  from  32°  to  T=480°,  and 
expand  the  volume  to  ^  =  240  cubic  feet  ? 

In  the  table  find  y  =  324.29  for  480°. 

Units  of  heat,       h  =  324.29  x  0.25  x  0.08042/160x240  =  1277.6. 

Example  13.  What  will  be  the  temperature  of  ^  =  36  cubic  feet  of 
carbonic  acid  heated  from  32°  and  volume  #=24  cubic  feet,  when 
h  =  140  units  of  heat  has  been  expended  on  it? 


0.221x0.1233/36x24 
This  corresponds  to  a  temperature  T=  185°  in  the  table. 

DRAFT  IN  CHIMNEYS. 

§  105.  The  draft  in  a  definite  chimney  depends  upon  the  temper- 
ature of  the  ascending  gases.  The  higher  the  temperature  is,  the 
lighter  will  the  gases  be,  and  consequently  create  a  stronger  draft 
under  the  fire-grate,  as  before  explained,  §  45. 

The  velocity  of  the  air  through  the  fire-grate  is 


Call  Z=(1=^) 2 

Then  the  velocity         F'  =  8/2T2T  .        .        .        .        .        3 


The  value  of  z  is  calculated  for  different  temperatures  of  the  gases 
in  the  chimney,  and  is  contained  in  column  z  in  Table  XXX. 

Example  3.  The  height  of  a  chimney  is  H  =  144  feet,  and  temper- 
ature of  the  gases  T=520°.  Required  the  velocity  of  the  draft 
through  the  fire-grate  ?  See  Table  XXX.  for  temperature  520°,  which 
corresponds  to  z  =  0.4977. 

V  =  8/144x4977  =  67.8  feet  per  second. 


HORSE-POWER   OF  CHIMNEYS. 


123 


TABLE  XXIX. 

Horse-power  of  Chimneys.    Formula  1,  \  26,  page  42. 

For  safety  this  table  gives  the  horse-power  about  25  per  cent,  less  than 

may  be  attained  in  practice. 

|| 

Area  of  chimney  in  square  feet  at  the  top. 

»i 

0.5 

1 

2 

4 

0 

10 

15 

20 

30 

40 

Feet. 

EP 

IP 

IP 

IP 

H> 

IP 

IP 

IP 

IP 

I?" 

20 

3.35 

6.7 

13.4 

26.8 

40.2 

67 

100.5 

134 

201 

268 

25 

3.7 

7.4 

14.8 

29.6 

44.4 

74 

111.0 

148 

222 

296 

30 

4.0 

8.0 

16.0 

32.0 

48.0 

80 

120.0 

160 

240 

320 

35 

4.25 

8.5 

17.0 

34.0 

51.0 

85 

127.5 

170 

255 

340 

40 

4.5 

9.0 

18.0 

36.0 

54.0 

90 

135.0 

180 

270 

360 

45 

4.75 

9.5 

19.0 

38.0 

57.0 

95 

142.5 

190 

285 

380 

50 

5.0 

10.0 

20.0 

40.0 

60.0 

100 

150.0 

200 

300 

400 

55 

5.2 

10.4 

20.8 

41.6 

62.4 

104 

156.0 

208 

312 

416 

60 

5.4 

10.8 

21.6 

43.2 

64.8 

108 

162.0 

216 

324 

432 

'65 

5.6 

11.2 

22.4 

44.8 

67.2 

112 

168.0 

224 

336 

448 

70 

5.8 

11.6 

23.2 

'46.4 

69.6 

116 

174.0 

232 

348 

464 

75 

6.0 

12.0 

24.0 

48.0 

72.0 

120 

180.0 

240 

360 

480 

80 

6.15 

12.3 

24.6 

49.2 

73.8 

123 

184.5 

246 

369 

492 

85 

6.35 

12.7 

25.4 

50.8 

76.2 

127 

190.5 

254 

381 

508 

90 

6.5 

13.0 

26.0 

52.0 

78.0 

130 

195.0 

260 

390 

520 

95 

6.65 

13.3 

26.6 

53.2 

79.8 

133 

199.5 

266 

399 

532 

100 

6.8 

13.6 

27.2 

54.4 

82.8 

136 

204.0 

272 

414 

544 

110 

7.1 

14.2 

28.4 

56.8 

85.2 

142 

213.0 

284 

426 

568 

120 

7.4 

14.8 

29.6 

59.2 

88.8 

148 

222.0 

296 

444 

592 

130 

7.65 

15.3 

30.6 

61.2 

91.8 

153 

229.5 

306 

459 

612 

140 

7.9 

15.8 

31.6 

63.2 

94.8 

158 

237.0 

316 

474 

632 

150 

8.15 

16.3 

32.6 

65.2 

97.8 

163 

244.5 

326 

489 

652 

160 

8.4 

16.8 

33.6 

67.2 

100.8 

168 

252.0 

336 

504 

672 

170 

8.65 

17.3 

34.6 

69.2 

103.8 

173 

259.5 

346 

519 

692 

180 

8.9 

17.8 

35.6 

71.2 

106.8 

178 

267.0 

356 

534 

712 

190 

9.2 

18.2 

36.4 

72.8 

109.2 

182 

273.0 

364 

546 

728 

200 

9.3 

18.6 

37.2 

74.4 

111.6 

186 

279.0 

372 

558 

744 

210 

9.5 

19.0 

38.0 

76.0 

114.0 

190 

2850 

380 

570 

760 

220 

9.7 

19.4 

38.8 

77.6 

116.4 

194 

291.0 

388 

582 

776 

230 

9.9 

19.8 

39.6 

79.2 

118.8 

198 

297.0 

396 

594 

792 

240 

10.1 

20.2 

40.4 

80.8 

121.2 

202 

303.0 

404 

606 

808 

250 

10.3 

20.6 

41.2 

82.4 

123.6 

206 

309.0 

412 

618 

824 

260 

10.5 

21.0 

42.0 

84.0 

126.0 

210 

315.0 

420 

630 

840 

270 

10.65 

21.3 

42.6 

85.2 

127.8 

213 

319.5 

426 

639 

852 

280 

10.8 

21.6 

43.2 

86.4 

129.6 

216 

324.0 

432 

648 

864 

290 

11.0 

22.0 

44.0 

88.0 

132.0 

220 

330.0 

440 

660 

880 

300 

11.15 

223 

44.6 

89.2 

133.8 

223 

334.5 

446 

669 

892 

310 

11.35 

22.7 

45.4 

90.8 

136.2 

227 

340.5 

454 

681 

908 

320 

11.5 

23.0 

46.0 

92.0 

138.0 

230 

345.0 

460 

690 

920 

330 

11.65 

23.3 

46.6 

93.2 

139.8 

233 

349.5 

466 

699 

932 

340 

11.8 

23.6 

47.2 

94.4 

1-41.6 

236 

354.0 

472 

708 

944 

350 

12.0 

24.0 

48.0 

96.0 

144.0 

240 

360.0 

480 

720 

960 

360 

12.15 

24.3 

48.6 

97.2 

145.8 

243 

364.5 

486 

729 

972 

370 

12.3 

24.6 

49.2 

98.4 

147.6 

246 

369.0 

492 

738 

984 

380 

12.45 

24.9 

49.8 

99.6 

149.4 

249 

373.5 

498 

747 

996 

390 

12.6 

25.2 

50.4 

100.8 

151.2 

252 

378.0 

504 

756 

1008 

400 

12.75 

25.5 

51.0 

102.0 

153.0 

255 

382.5 

510 

765 

1020 

124 


PERMANENT    GASES. 


TABLE    XXX. 
Physical  Properties  of  Permanent  Gases. 

Temp. 

hte 

rv 

pv 

T-t 

V* 

1-L 

X 

Tffi: 

PV 

pv 

T-t 

V* 

«4 

TF°3?: 

PV 
pv 

T-t 

Vx 

l-L 

x 

T 

X 

y 

Z 

T 

X 

y 

z 

T\    x 

y 

Z 

-180 

0.5700 

-  280.9 

-  0.261 

82 

1.0000 

0.0000 

O.OOdO 

82 

1.1014 

47.1)4.", 

0.0920 

-170 

0.5903 

-  262.9 

-0.306 

33 

1.0020 

0.9990  0.0019 

83 

l.KKM  48.552 

0.0935 

-160 

0.6106 

-245.8 

-  0.362 

34 

1.0040 

1.9960 

).oo:;«.i 

84 

1.105449.459 

0.0954 

-150 

0.6308 

-229.3 

-0.415 

35 

1.0061 

2.9909 

0.0059 

sr> 

1.1075  50.362 

0.0969 

-140 

0.6511 

-213.2 

-0.464 

36 

1.0081 

3.9839 

0.0079 

86 

.1095  51.266 

0.0986 

-130 

0.6714 

-197.7 

-0.511 

37 

1.0101 

4.9750 

0.0099 

87 

1.111552.168 

0.0999 

-120 

0.6917 

-  187.8 

-  0.554 

38 

1.0121 

5.9640 

0.0118 

88 

1.1135 

r,;;.oi;<) 

0.1019 

-110 

0.7120 

-168.3 

-  0.595 

39 

1.0142 

6.9508 

0.0187 

89 

1.1156 

53.91)6 

0.1035 

-100 

0.7322 

-154.3 

-  0.634 

40 

1.0162 

7.9360 

0.0157 

90 

1.117654.851 

0.1051 

-90 

0.7524 

-  140.7 

-0.671 

41 

1.0182 

8.9192 

0.0176 

91 

1.1196  55.760 

0.1069 

-80 

0.7727 

-  127.4 

-  0.706 

42 

1.0203 

9.9000 

0.0195 

92 

1.1217  156.652 

0.1083 

-70 

0.7930 

-114.5 

-  0.739 

43 

1.0223 

10.880 

0.0215 

n:; 

1.1237 

57.555 

0.1099 

-60 

0.8133 

-102.0 

-0.770 

44 

1.0243 

11.857 

0.0234 

94 

1.1257 

58.436 

0.1118 

-50 

0.8336 

-  89.82 

-0.800 

45 

1.0264 

12.834 

0.0253 

95 

1.1277 

59.326 

0.1130 

-40 

0.8540 

-77.91 

-  0.829 

46 

1.0284 

13.805 

0.0272 

96 

1.1297 

60.214 

0.1149 

-30 

0.8742 

-66.31 

-0.856 

47 

1.0304 

14.777 

0.0291 

1)7 

1.1318 

61.098 

0.1165 

-20 

0.8945 

-54.98 

-0.882 

48 

1.0325 

15.746 

0.0315 

98 

1.1338 

61.983 

0.1179 

-10 

0.9148 

-.43.91 

-0.907 

49 

1.0345 

16.714 

0.0329 

99 

1.1358 

62.867 

0.1191 

0 

0.9352 

-33.01 

-  0.930 

50 

1.0365 

17.680 

0.0349 

100 

1.1378 

63.749 

0.1210 

1 

0.9371 

-  32.06 

-0.933 

51 

1.0385 

18.666 

0.0365 

101 

1.1399 

64.627 

0.1227 

2 

0.9391 

-  30.96 

-  0.935 

52 

1.0406 

19.606 

0.0389 

102 

1.1419 

65.506 

0.1243 

3 

0.9411 

-29.89 

-0.937 

53 

1.0426 

20.567 

0.0402 

103 

1.1439 

66.384 

0.1257 

4 

0.9432 

-28.83 

-  0.939 

54 

1.0446 

21.575 

0.0429 

10411.1459 

67.260 

0.1273 

5 

0.9452 

-27.77 

-  0.942 

55 

1.0466 

22.482 

0.0444 

105 

1.1480 

68.132 

0.1288 

6 

0.9472 

-26.72 

-  0.944 

56 

1.0487 

23.463 

0.0464 

106 

1.1500 

69.005 

0.1304 

7 

0.9492 

-  25.67 

-  0.946 

57 

1.0507 

24.390 

0.0485 

107 

1.1520 

69.877 

0.1319 

8 

0.9513 

-  24.62 

-  0.949 

58 

1.0527 

25.341 

0.0503 

108 

1.1541 

70.745 

0.1334 

9 

0.9533 

-  23.56 

-0.951 

59 

1.0547 

20.21)0 

0.0521 

109 

1.1561 

71.613 

0.1349 

10 

0.9554 

-  22.51 

-  0.953 

60 

1.0567 

27.260 

0.0539 

110 

1.1581 

72.481 

0.1364 

11 

0.9577 

-21.46 

-0.956 

61 

1.0588 

28.184 

0.0557 

111 

1.1602 

73.344 

0.1379 

12 

0.9594 

-20.42 

-  0.958 

62 

1.0608 

29.128 

0.0574 

112 

1.1622  74.208 

0.1393 

13 

0.9614 

-  19.38 

-  0.960 

63 

1.0628 

30.070 

0.0592 

113 

1.1642  75.072 

0.1408 

14 

0.9635 

-18.34 

-  0.962 

64 

.0649 

31.010 

0.0610 

114 

1.1663  75.929 

0.1423 

15 

o.'.t*  555 

-  17.30 

-  0.964 

65 

.0669 

31.949 

0.0627 

115 

1.1683  76.790 

0.1438 

16 

0.9675 

-16.26 

-0.966 

66 

1.0689 

32.896 

0.0645 

116 

1.1703^77.648 

0.1452 

17 

0.9676 

-15.23 

-0.966 

67 

1.0709 

33.822 

0.0662 

117 

1.172478.502 

0.1469 

18 

0.9716 

-14.22 

-0.971 

68 

.0720 

34.770  0.0671 

118 

1.174479.358 

0.1486 

19 

0.9734 

-13.18 

-  0.972 

69 

1.0740 

35.703!  0.0688 

119 

1.1764  80.212 

0.1499 

20 

0.9756 

-12.15 

-0.975 

70 

1.0760 

36.633  10.0706 

120 

1.178481.066 

0.1515 

21 

0.9777 

-11.13 

-0.977 

71 

1.0780 

37.563  0.0723 

121 

1.180581.914 

0.1528 

22 

0.9797 

-10.11 

-0.979 

72 

1.0811 

38.470  0.0749 

122 

1.1825182.764 

0.1541 

23 

0.9817 

-  9.089 

-0.981 

73 

1.0831 

39.396  0.0766 

123 

1.184583.621 

0.1559 

24 

0.9837 

-  8.069 

-0.983 

74 

1.0851 

40.320  0.0783 

124  1.1866  84.457 

0.1571 

25 

0.9856 

-7.051 

-0.985 

75 

1.0871 

41.2M)  0.0800 

125  1.1886  85.303 

0.1586 

26 

0.9878 

-6.031  1-0.988 

76 

1.0892  42.160  0.0817 

126  1.1906  86.148  0.1601 

27 

0.9898 

-5.029;  -0.990 

77 

1.09i2  43.079  0.0833 

127  1.192786.9880.1615 

28 

0.9917 

-4.017 

-0.991 

78 

1.0932  43.995  '0.0870 

128  1.1947  87.830  0.1629 

29 

<).<i<»;;<) 

-3.010 

-  0.994 

79 

1.0953  44.940  0.0869 

121)  1.1967  88.671 

0.1642 

30  !  0.9957 

-2.005  -0.995 

80 

1.0973:45.822  0.0883 

130  1.1987  89.510 

0.1657 

31    0.9979  -1.002  -0.998 

81 

1.0993  46.734  0.0899 

131  1.200890.3740.1670 

PERMANENT   GASES. 


125 


TABLE    XXX. 

Physical  Properties 

of  Permanent 

Gases. 

T      1 

PV 

T-t 

, 

Temp. 

PV 

T-t 

l 

Temp. 

PV 

T-t 

, 

Fahr. 

pv 

V* 

X, 

Fahi. 

pv 

V* 

z" 

Fahir. 

pv 

V* 

~x 

T 

X 

y 

Z 

T 

X 

y 

Z 

T 

X 

y 

Z 

132  1.2028 

91.152 

0.1686 

1S2 

1.3041 

131.34 

0.2331 

232 

1.4056 

168.70 

0.2885 

133! 

1.2048 

92.0160.1699 

183 

1.3062 

132.11 

0.2343 

233 

1.4076 

169.42 

0.2895 

134  1.2069  92.846  0.1714 

184 

1.3082 

132.88 

0.2355 

•'.",1 

1.4096 

170.14 

0.2905 

135 

1.20S') 

93.579 

o.l  72s 

185 

1.3102 

133.65 

0.2367 

2:55 

1.4116 

170.86 

0.2915 

136  1.2109  94.5100.1742 

186 

1.3122 

134.42  0.2378 

236  1.4137 

171.58 

0.2925 

137 

1.212995.3400.1755 

1S7 

1.3143!  135.19|0.2390 

2;  17 

1.4157 

172.29 

0.2935 

138 

1.215096.1650.1769 

188 

1.3163 

135.961  0.2402 

2:;s 

1.4177 

173.01 

0.2945 

139 

1.2170  96.993  0.1782 

189 

1.3184 

136.730.2414 

239 

1.4198 

173.73 

0.2955 

140 

1.2190  97.819'0.1796 

190 

1.3204 

137.500.2426 

240 

1.4218 

174.44 

0.2965 

141 

1.2211 

98.640  0.1809 

191 

1.3224 

138.27  0.2438 

241 

1.4238  175.15 

0.2976 

142 

1.2231 

99.4630.1823 

192 

1.3244 

139.04  0.2449 

242 

1.4258  175.86 

0.2986 

143 

1.2251 

100.290,1836 

193 

1.3265 

139.81 

0.2461 

243 

1.4279  176.57 

0.2996 

144 

1.2272 

101.10'0.1849 

194!  1.3285 

140.58 

0.2472 

2441.4299 

177.28 

0.3006 

145 

1.221)2 

101.92  0.1863 

195 

1.3305  141.35 

0.2483 

245 

1.4319 

177.99  0.3016 

1461  1.2312 

102.740.1876 

196 

1.3326  142.12  0.2494 

,246 

1.4340 

178.70  0.3026 

147 

14S 

1.2333 
1.2353 

lo:;,15  0.1889 
104.37  0.1902 

197  1.3346  142.89  0.2506 
198  1.3366)143.66  0.2517 

247 

248 

1.4360179.410.3036 
1.4380  180.12  '  0.3046 

149 

1.2373 

105.180.1915 

199 

1.3386 

144.42  0.2529 

249 

1.4401 

180.83  0.3056 

150 

1.2393 

106.000.1928 

200 

1.3407 

145.19  0.2541 

250 

1.4421 

181.  54'  0.3066 

151 

1.2414 

106.81 

0.1941 

201 

1.3427 

145.95  !  0.2553 

251 

1.4441 

182.240.3076 

152:1.2434 

'107.620.1954 

202 

1.3447  146.70  0.25r>5 

i252|  1.4462  182.94 

0.3086 

153  1.2454 

108.430.1967 

203 

1.3468 

147.44 

0.2575 

1  253  1.4582 

183.64 

0.3096 

154 

1.2475  109.230.1984 

204 

1.3488 

148.18 

0.2586 

254 

1.4402 

184.34 

0.3104 

155 

1.241)5  110.04  0.1996 

205 

1.3508 

!  148.92 

0.2597 

255 

1.4522 

185.04 

0.3112 

156 

1.2515 

110.84 

0.2003 

206 

1.3529 

149.660.2608 

256 

1.4543 

185.74 

0.3122 

157 

1.2535  111.650.2022 

:207 

1.3549  150.39  0.2619 

257 

1.4563 

186.44  0.3131 

158 

1  .2556 

112.450.2035 

208 

1.3569 

151.12  0.2630 

'258 

1.4583 

187.14  0.3141 

159 

1.2576 

113.25 

0.2047 

'209 

1.3589 

151.85 

0.2641 

259 

1.4604 

187.84 

!  0.31  51 

160 

1.2596  114.05  0.2060 

i210|l.3610|  152.58 

0.2652 

260 

1.4624 

!  188.54  0.3159 

161 

1.2616:114.850.2072 

211 

1.3630  153.32 

0.2663 

261 

1.41)44 

189.24  0.3169 

162 

1.2637 

115.640.2086 

!  212  i  1.3650;  154.06 

0.2674 

262 

1.4664  189.93  0.3178 

163 

1.2657 

116.44,0.2098 

;213 

1.3670  154.80 

0.2685 

263 

1.4685 

il90.62iO.3187 

164 

1.2677 

117.24 

0.2111 

214 

1.3691 

155.54 

0.2695 

264 

1.4705 

1191.32 

0.3199 

165 

1.2697:118.040.2123 

215 

1.37111156.28 

0.2705 

265 

1.4725 

192.01 

0.3209 

166  1.27171118.83  0.2136 

216 

1.3731  157.02 

0.2716 

266 

1.4745  192.70'0.3217 

167 

1.2738!  119.62  0.21  41) 

217 

1.3751  157.76 

0.2727 

267 

1.4766 

193.39;  0.3227 

168 

1.  2758  j  120.41 

0.2161 

:218 

1.3772  158.50 

0.2737 

268 

1.4786 

194.08  0.3236 

169 

1.2778 

J121.20  0.2173 

219 

1.37921159.24 

0.2748 

269 

1.4806)  194.77  i  0.3246 

170 

1.2798|  121.98  0.2186 

220 

'  1.  38  12  '  159.97 

0.2758 

1270 

1.48261195.46 

0.3255 

171 

1.2818  122.77  0.2198 

22 

1.3832  160.71 

0.2768 

271 

1.4847 

196.15  0.3265 

172 

1.28391  123.56  0.2210 

222 

1.3853  161.45  0.2781 

272 

1.4867 

1  196.84 

;  0.3274 

173 

1.2859:124.350.2222 

2l-'" 

1.3873  162.19  i  0.2792 

273 

1.4887 

197.530.3284 

174J1.287J 

i  125.  13  0.2236 

224 

:  1.  3893  1  162.93  0.2803 

274 

1.4907 

198.22  0.3293 

175i  1.28991125.91  0.2248 

22' 

:  1.3913,  163.67 

0.2814 

275 

1.  4D28  198.90  0.3302 

176 

1.2920!  126.69  0.2259 

:  226'  1.3934  164.41 

0.2824 

278 

1.4948  199.58  0.3310 

177 

1.294C 

)  127.4- 

0.2271 

227 

1  .'>1)5- 

165.15 

0.2*34 

277 

1  1.4968 

200.2' 

0.3319 

178  1.2960  128.25  0.2283 

,228  1.3974165.880.2844 

278 

1.4988  200.94:0.3327 

179  1.2980  129.02  0.2295 

221)  1.3995  166.61  0.2854 

279 

1.5009201.620.3337 

180;  1.3001;  129.80  0.2307 

230i  1.4015!  167.25  0.2864 

2SO 

1.5029  202.30  0.3346 

181 

1.3021  130.57  0.2329 

1231 

1.4035  '167.  98!  0.2874 

281 

1.5049  202.98  0.3355 

126 


PERMANENT    GASES. 


TABLE    XXX. 

Physical  Properties  of   Permanent 

Gases. 

Temp. 

PV 

T-t 

l-l 

PV 

T-t 

l-L 

Temp. 

PV 

L=* 

l_» 

Kahr! 

pv 

V* 

• 

pv 

V* 

X 

Fab?. 

pv 

V* 

X 

T 

282 

1.5070 

y 

203.66 

0.3363 

1        X 

1.6084 

y 

•_':;<;.:,.-, 

z 
0.3781 

T 

382 

X 

1.7097 

267*71 

0.4150 

288 

1.5090  204.34  0.3372 

1.6104237.19 

0.3788 

383 

1.7118  2«S.:W 

0.4157 

2S4 

1.5110  205.02 

0.3381 

1  1.61  24  237.83 

0.3796 

:w4 

1.7138 

268.94  0.41641 

2S5 
2S(i 

1.5131  205.70J0.3390 
1.5151  206.37  0.3399 

1.6144 
1.6165 

238.43 
239.11 

0.3804 
0.3811 

385 

386 

1.7158  269.551  0.417  li 
1.7179  270.16  0.4179 

287 

1.5171 

207.04 

0.3407 

1.6185 

239.75 

0.3819 

387  1.71991270.77 

0.4185 

288 

1.5192 

207.71 

0.3416 

1.6205 

240.39 

0.3827 

388  1.7219:271.38  0.4192 

289 

1.5212 

208.38  0.3425  1 

1.6226 

241.02 

0.3836 

389 

1.  72  10  27  1.99  0.4199 

290 

1.5232 

209.05  0.3433 

01.6246 

241.65 

0.3845 

390 

1.7260  '272.50  0.4206 

291 

1.5252 

209.720.3442 

1.6266 

242.28 

0.3852 

391 

1.7280  273.100.4212 

292 

1.5273 

210.39  0.3458 

2  1.6286 

242.91 

0.3859 

392 

1.7301 

273.70 

0.4219 

293 

1.5293 

211.06  0.3459 

3  1.6307 

243.54 

0.3868 

893 

1.7321 

274.30 

0.4226 

294 

1.5313 

211.73  0.3468 

4  1.6327 

244.17 

0.3875 

394 

1.7341 

274.90 

0.4232 

295 
296 
297 

1.5334  212.40  0.3476 
1.5354  213.07  10.3485 
1.53741213.74  0.3493  ' 

o  1.6347 
6  1.6368 

7  1.6388 

244.80 
245.43 
246.06 

0.3882 
0.3889 
0.3897 

395 
396 
397 

1.7361  275.49 
1.7382  276.09 
1.74021276.69 

0.4239 
0.4246 
0.4252 

298 

1.5395  214.40  0.3501 

8  1.6408 

246.69 

0.3906 

398 

1.7422i277.29 

0.4259 

299 

1.5415  215.06 

0.3510  i 

91.6429  247.31 

0.3913 

399 

1.7443 

277.89 

0.42155 

300 

1.5435  215.72'0.3518 

Oi  1.6449  !  247.93 

0.3920 

400 

1.7463 

278.48  10.4272 

301 

1.5455  216.38 

0.3527 

1  1.6469  248.56 

0.3928 

401 

.7483 

279.0810.4279 

302 

1.5476,217.040.3539 

2  1.6490  249.19 

0.3935 

402 

1.7504 

27!Ui,S  0.428.-, 

303 

1.5496217.700.3548! 

31.6610249.82 

0.3942 

403 

1.7524280.27!0.4292 

304 

1.5516>218.36 

0.3556  1 

4  1.6530  250.45 

0.3950 

404 

1.7544 

•280.8(5  0.4-29S' 

305 
306 

1.5537 
1.5557 

219.02!0.3584 

219.68  0.3573 

->  1.6551  251.08 
6  1.65711251.70 

0.3957 
0.3964 

405 
406 

1.7564281.450.4305 

1.7585  282.04  0.4314 

307 

1.5577 

220.34!  0.3581 

7  1.6591 

2.32.32 

0.3971 

407 

1.7605  2S2.M 

0.4320 

308 

1.5597 

221.000.3589 

8  1.6611 

252.94 

0.3979 

408 

1.7625 

283.22 

0.4325 

309 

1.5618 

221.65  0.3597 

911.6632 

253.56 

0.3986 

409 

1.7646 

283.81 

o.4:;:;:> 

310 

1.5638 

222.30 

0.3605 

01.6652 

254.18 

0.3993 

410 

1.7666 

•2S4.40  0.4340 

311 

r.5658  222.96  0.361  4  ' 

1  1.6672 

254.80 

0.4001 

411  1.7686  284.9~9!  0.4346 

312 

1.5678223.61  0.3622 

2  1.6692 

255.42 

0.4008 

412 

1.7706 

285.58,  0.4353 

313 

1.5699224.27  0.3630, 

31.6713 

256.04 

0.4015 

413 

1.7727 

286.17  0.4359 

314 

1.5719224.930.3638 

4  l.()7.4;:i 

256.66 

0.4022 

414 

1.7747 

286.76 

0.4365 

315 

1.5739  225.58  0.3646 

5!  1.6753 

257.28 

0.4029 

415 

1.7767 

287.35 

0.4372 

316 
317 
318 

1.5759 
1.5780 
1.5800 

226.23  0.3654  ; 
226.880.3662; 
227.530.36701 

6|1.6773 
7  j  1.6794 
8|1.6814 

257.90 
258.51 
259.12 

0.4036 
0.4043 
0.4051 

416 
417 

418 

1.7787  287.94  0.4378 
1.7808  288.43  0.4384 
1.7828  289.01  0.4391 

319 

1.5820  228.28  0.3678 

911.6834 

259.740.4058 

419 

1.7848  289.59  10.4397 

320 

1.5840  228.83 

0.3686 

Oi  1.6854 

260.36  '0.4065 

420 

1.7868 

•>!)()  .27  0.4403 

321 

1.58611229.480.3694 

1  1.6875 

260.97 

0.4072 

421 

1.7889  290.85!0.4410 

322 

1.58811230.13 

0.3702 

21.6895261.58 

0.4079 

422 

1.7909 

291.430.4416 

323 

1.5901  j230.78(0.3710 

31.6915262.190.4085 

423 

1.7929292.01:0.4422 

324 

1.5922  '231.  42  0.37  18  i 

41.6935262.800.4096 

424 

1.7950  292.59!  0.4428 

325 
326 

1.5942232.060.3726! 
1.5962  232.7  11  0.3734! 

51.6956263.41  0.4103 
61.6976264.020.4110 

425 
426 

1.7970  293.17  0.4434 
1.7990  293.75!0.4441 

327 

1.5982 

233.350.3741 

7  1.6996  264.63  0.4116 

427 

1.8010  294.33  '0.4447 

328 

1.6003  2:::;.<H 

0.3749  i 

8  1.7016:265.24,0.4123 

428 

1.8031 

294.91  0.4453 

329  1  1.6023  234.63  0.3757 

91.7037 

•2I15.85 

0.4130 

429 

1.8051 

295.49 

0.4459 

330 

1.6043  2:15.27 

0.3765 

0  1.7057 

•2f.li.4fi 

0.4137 

430 

1.8071 

296.07 

0.446,5 

331  1.6063  235.91  '0.3773 

1  1.7077  267.09 

0.4144 

431  1.8091 

296.65  0.4471 

PERMANENT   OASES. 


127 


TABLE    XXX. 

Physical  Properties  of  Permanent  Gases. 

a 

PV 

pv 

T-t 

V* 

X 

BE 

PV 

pv 

T-t 

V* 

l-L 

X 

Tffi 

PV 

pv 

T-t 

V* 

l_ji_ 

X 

T 

X 

y 

z 

T 

X 

y 

Z 

T 

X 

y 

Z 

4:5-J 

1.8112 

297.23 

0.4477 

482 

1.9126 

325.39 

0.4771 

820 

2.5980 

488.87 

0.6150 

433 

1.8132 

297.81 

0.4483 

483 

1.9146 

325.94  0.4777 

830 

2.6183 

493.14 

0.6180 

434 

1.8152 

298.39 

0.4490 

484 

1.9166 

326.49  0.4783 

840 

2.6385 

497.43 

0.6209 

435 

1.8173 

2<tS.<)7 

0.4496 

485 

1.9187 

327.04  0.4789 

850 

2.6588 

501.66 

0.6239 

i:;t; 

1.8193  299.54 

0.4502 

486 

1.9207 

327.59 

0.4794 

860 

2.6791 

505.88 

0.6267 

4:;7 

1.8213300.11 

0.4508 

487 

1.9227 

328.14 

0.4799 

870 

2.6994 

510.07 

0.6294 

-i:;s 

1.8234 

:;oo.i;s 

0.4524 

488 

1.9248 

328.69  0.4805; 

880 

2.7197 

514.23 

0.6323 

4:w 

1.8254  301.25 

0.4520 

489 

1.9268 

82U.24  0.4811 

890 

2.7399 

518.36 

0.6850 

440 
441 

1.8274  301.82 
1.82941302.39 

0.4526 
0.4532 

490 
491 

1.9288  329.78 
1.9309330.33 

0.4816' 
0.4821 

900 
910 

2.7602522.450.6376 
2.7805  526.5410.6403 

442 
443 

1.83151302.96  0.4538 
1.8335  303.53  0.4544 

492  1.93291  330.88 
493!  1.9349  331.  43 

0.4827: 
0.4832 

920 
930 

2.8008 
2.8211 

530.610.6429 
534.660.6455 

444 

1.8355 

304.10 

0.4550 

4<U  L.9369  331.98 

0.4838' 

940 

2.8413538.7110.6480 

445 

1.8376  304.67 

0.4558 

495  1.9390  332.52 

0.4843; 

!)--,() 

2.8616J542.67I0.6504 

446 

1.8396305.24 

0.4564 

496  1.9410 

333.06 

0.4847 

960 

2.8819  546.66 

0.6529 

447 

1.8416  305.81 

0.4570 

497 

1.9430 

333.60 

0.4852 

970 

2.9022 

550.60 

0.6554 

448 

1.8436306.37 

0.4576 

498  1.9451 

334.14 

0.4857; 

980 

2.9225554.52 

0.6577 

449  j  1.8457 

306.94 

0.4581 

499  1.9471 

334.68 

0.4863 

990 

2.9427  558.45 

0.6601 

450 

1.8477 

307.51 

0.4587 

500  1.9491 

335.22 

0.4869 

1000 

2.9630 

562.36 

0.6624 

451 

1.8497 

308.08 

0.4593 

510 

1.9694 

340.60 

0.4921| 

1010 

2.9833  566.24 

0.6647 

452 

1.8618308.65 

0.4599 

520 

1.9898 

345.95 

0.4977 

1020 

3.0036  570.09  0.6670 

453 

1.8538  :',(>;).±J 

0.4605 

530  2.0102;  351.  26 

0.5024. 

1030 

3.0239 

573.94  0.6692 

454!  1.8558  309.79 

0.4611 

540 

2.0302  356.53 

0.5073 

1040 

3.0441 

577.73  0.6714 

455 

1.8579  31o..'5o 

0.4617 

550 

2.0505 

361.75  0.5120 

1050 

3.0644 

581.530.6736 

45611.8599  310.91 

0.4623 

560 

2.0708 

366.93  0.5171 

1060 

3.0847 

585.32  0.6758 

457  1.8619  311.47 
458  1.8639  !  312.03 

0.4629 
0.4635 

570 

580 

2.0909 
2.1113 

372.06 
377.16 

0.5217 
0.5262 

1070 
1080 

3.1050 
3.1253 

589.08  0.6779 
592.82  0.6799 

459 

1.8660312.59 

0.4641 

590 

2.1316 

382.28 

0.5308 

1090 

3.1455  596.54  0.6820 

460 

1.8680  313.15 

0.4647 

600 

2.1519 

387.20 

0.5353 

1100 

3.1658 

600.24 

0.6841 

461 

1.8700 

313.71 

0.4652 

610 

2.1721 

392.18 

0.5395 

1110 

3.1861 

603.92!  0.6861 

462  1  1.8720 

314.27 

0.4657 

620 

2.1924 

397.13 

0.5437, 

1120 

3.2064 

607.62  0.6880 

4(53  1.S741 

314.83 

0.4663 

630 

2.2127 

402.03 

0.5481 

1130 

3.2267 

611.27 

0.6901 

464 

1.8761 

315.39 

0.4669 

640 

•2.-r>2!)  406.89 

0.5521 

1140 

3.2469 

614.92 

0.6920 

465  1.8781 

315.95 

0.4675 

650J2.2532  411.71 

0.5561 

1150 

3.2672 

618.52  0.6938 

466  1.8801  316.51 

0.4681 

660  2.27  34  !  416.50 

0.5601 

1160 

3.2875 

622.13  0.6957 

467 

1.8822 

317.07  O.l'isi; 

670  2.29381421.25 

0.5640 

1170 

3.3078 

625.73  0.6976 

468 
469 

1.8842  317.63  0.4692 
1.8862  318.19  0.4697 

6802.3141425.98 
690  2.3343|430.67 

0.5678: 
0.5715' 

1180 

1190 

3.3281 
3.3484 

629.32  0.6994 
632.90  0.7013 

470;  1.8882  31  8.75 

0.4703 

700  2.3545  ;  435.34 

0.5752 

1200 

3.3687 

636.38  0.7031 

471 

1.8903319.31 

0.4709 

710  2.3749  439.88  0.5789| 

1300 

3.5714 

671.08  0.7199 

472 

1.89231819.87 

0.4714 

720  2.3952  444.52  0.5824 

1400 

3.7743  704.74  0.7350 

473 

1.8943:320.43 

0.4720 

730  2.4155;449.11  10.5859 

1500 

3.9770  737.35iO.7485 

474 

1.8963  320.99 

0.4726 

740  2.4357  453.67  0.5894 

1600 

4.1798  766.95  0.7608 

475 

1.8984 

321.54 

0.4731 

750  2.4560  458.15 

0,-><>2S 

1700 

4.3826  797.49  0.7768 

476  ;  1.9004 

322.09 

0.4736 

760  2.4763  462.60  0.5961 

1800  4.5854  826.60  0.7818 

477 

1.9024 

322.64 

0.4742 

7702.4966  467.03  0.5993 

19004.7882854.450.7911 

478 

1.9044 

323.19 

0.4747 

780'2.5169  471.44  0.6026 

2000  4.9910  880.91  0.7996 

479 

1.9065  323.74 

0.4752 

790  2.5371  475.84  0.6058 

21005.1938906.760.8074 

480  1.9085  324.29  0.4758 
4811.91051324.840.4764 

800  2.5574  480.24  !  0.6089 
810!2.5777I484.56  0.6120 

•2200  .-..  3966  ,931.72  0.8147 
2300  5.5994  957.80  0.8213 

128  PHYSICAL  PROPERTIES   OF  AIR. 

COMPRESSION  AND  EXPANSION  OF  A 
DEFINITE  WEIGHT  OF  AIR. 

§  107.  This  subject  does  not  yet  seem  to  have  been  satisfactorily 
treated,  either  by  experiments  or  mathematics,  for  which  reason  the 
following  formulas  and  tables  can  be  considered  approximately 
correct  only  within  our  limit  of  practice.  The  assumption  of  the 
existence  of  an  absolute  zero  at  -461°,  and  that  gases  are  still 
permanent  at  that  temperature,  does  not  appear  to  agree  with  the 
experiments  on  the  compression  and  expansion  of  a  definite  weight 
of  air.  In  order  to  make  the  exponents  of  the  formulas  of  even 
numbers,  the  temperature  -  343°  is  herein  adopted  as  an  ideal  zero, 
not  with  assumption  that  this  is  an  absolute  zero,  but  it  may  be  the 
temperature  about  which  air  condenses  to  liquid  or  freezes  solid  and 
its  pressure  ceases. 

It  is  supposed  in  the  following  formulas  that  a  definite  weight  of 
air  is  enclosed  in  a  vessel,  which  volume  can  be  increased  or  dimin- 
ished without  losing  or  gaining  any  weight  of  the  air  enclosed 
therein,  and  that  no  heat  is  lost  or  gained  by  conduction  or  radiation 
to  or  from  the  sides  of  the  vessel. 

V=  volume  and  t  =  temperature  of  the  air  to  be  compressed  or 
expanded  to  the  volume  ^  of  temperature  T. 

Thus,  when  the  air  is  compressed,  the  small  volume  is  ^  and  the 
high  temperature  is  T;  but  when  the  air  is  expanded,  ^  means  the 
large  volume  and  T  the  lowest  temperature. 


=  (T  +  343),  the  ideal  temperature  of  the  volume  ^. 
t  =  (t  +  343),  the  ideal  temperature  of  the  volume  V. 

\  108.  VOLUME  AND  TEMPERATURE. 


COMPRESSION  AND  EXPANSION  OF  AIR.  129 

Compression  of  Air. 

Example  3.  To  what  volume  must  V=  9  cubic  feet  of  air  of  t  =  62° 
be  compressed  in  order  to  increase  the  temperature  to  T=552°? 

t  =  62 +  343  =  405°.         C  =  552 +  343  =  895°. 

Volume,     if  =  9  (  —  Y  =  1.843  cubic  feet. 
V  895  / 

Example  4-  A  volume  of  air  ^=5  cubic  inches  of  t  =  75°  is  to  be 
compressed  to  ^  =  0.35  cubic  inches.  Required  the  temperature  of 
the  compressed  volume  ? 

t  =  75 +  343  =  418°. 

Temperature,         C  =  41 8-J— -—  =  1607.2. 
»  0.35 

T=  1607.2  -  343  =  1264.2°,  the  temperature  required. 

Expansion  of  Air. 

Example  4-  A  volume  of  air  %f=  12  cubic  feet  and  of  temperature 
t  =  57°  is  to  be  expanded  to  ^  =  36  cubic  feet.  Required  the  temper- 
ature of  the  expanded  volume  ? 

Ideal  temperature,        C  =  400X/—  =  230.95°. 
\  36 

343  -  231  =  - 112°,  the  required  temperature. 

Example  3.  How  much  must  air  of  t  =  32  be  expanded  in  order  tc 
reduce  the  temperature  to  T=  -  80°  ? 

C=  343 +  80  =  163°        and        t  =  343  +  32  =  375°. 

/  S75  V 
Volume,        ^  =(  — ;~  1  =  5.293  times  the  primitive  volume. 


\  109.  PRESSURE  AND  TEMPERATURE. 

p  i  ar  s  f  t 

F 


i  ar  \s 

-(T] 


P=  pressure  at  temperature  C  or  T. 
p  =  primitive  pressure  at  temperature  t  or  t. 


130  PHYSICAL  PROPERTIES  OF  AIR 


/       The  pressures  mean  above  vacuum, 


Compression  of  Air. 

Example  6.  A  volume  of  air  of  p  =  14.7  pounds  pressure  and  of 
temperature  £  =  52°  is  to  be  compressed  until  the  temperature  be- 
comes T=360°.  Kequired  the  pressure  of  the  air  at  that  temper- 
ature ? 

Pressure,        P=  14.7/  —  T  =  96.84  pounds. 


Example  7.  A  volume  of  air  of  pressure  p  =  16  pounds  to  the  square 
inch  and  of  temperature  t  =  45°  is  to  be  compressed  to  P  =  80  pounds 
per  square  inch.  Required  the  temperature  of  the  compressed  air  ? 

t  =  343 +  45  =  388°. 
Ideal  temperature,         C  =  388  J/—  -  663.48°. 

T=  663.48  -  343  =  320.48°,  the  temperature  required. 

Expansion  of  Air. 

Example  6.  Air  of  pressure  p  =  14.7  pounds  and  t  =  48°  is  to  be 
expanded  until  the  temperature  becomes  T=  -12°.  Required  the 
pressure  of  the  expanded  air  ? 

Pressure,         P- 14.7 (  -  -  )  =8.9181  pounds. 


Example  7.  A  volume  of  air  of  pressure  p  =  15  pounds  and  temper- 
ature t  =  SO°  is  to  be  expanded  until  the  pressure  becomes  P=5 
pounds  to  the  square  inch.  Required  the  temperature  of  the  ex- 
panded air? 

t  =  343 +  80  =  423. 

•nr 

Ideal  temperature,         C  -  423^1  —  =  293.3°. 
\  15 

The  required  temperature,  T=  293.3  -  343  =  49.7°  below  Fahr.  zero. 


COMPRESSION  AND  EXPANSION  OF  A  IE.  131 


g  110.  VOLUME  AND  PRESSURE. 

f#        3/P 


VI 


'        n#7 


8 

9 

10 


Compression  of  Air. 

Example  9.  A  volume  of  air  #=18  cubic  feet  of  pressure  p  =  15 
ffounds  is  compressed  to  P  =  25  pounds  to  the  square  inch.  Required 
the  volume  of  the  compressed  air  ? 

Volume,     y  =>  l&Jf  ^  \  =  12.805  cubic  feet. 
'  V  25  / 

Example  10.  A  volume  of  air  #=24  cubic  inches  and  jo  =  15 
pounds  is  compressed  to  "^  =  6  cubic  inches.  Required  the  pressure 
of  the  compressed  volume  ? 

//  24  V 
Pressure,       P=  15* /(  — -  )  =  120  pounds  to  the  square  inch. 


'Me 


Expansion  of  Air. 

Example  9.  A  volume  of  air  #=5  cubic  metres  and  of  pressure 
p  =  l  atmosphere  is  to  be  expanded  to  P=0.25  of  an  atmosphere. 
Required  the  volume  of  the  expanded  air? 


Volume  V  =  5  V  ( I  =  12.6  cubic  metres. 

»  y  0.25  / 

Example  10.  What  will  be  the  pressure  of  air  expanded  to  5  times 
its  original  volume  ? 

TV 
Pressure,  ^=\/(    )  =^-299  of  the  original  pressure. 


132  PHYSICAL  PROPERTIES  OF  AIR. 

gill.  WORK    OF   COMPRESSION. 

The  differential  work  of  compression  will  be 

,  but  P-p 


When  W=lfr,   then   k=0,   and 

P\—+  c=  °>  of  which  C--2pV. 

\  ^ 

The  work    k  =  2  p  \l— 2  p  V, 


Let  %f  and  ^  be  expressed  in  cubic  feet  and  p  =  14.7  pounds  to  the 
square  inch. 

K=  work  in  foot-pounds  per  cubic  feet  of  V  compressed  to  rf. 

2  p  =  2x!44x  14.7  =  4233.6. 
K=  4233.6^-^^  -A 12 

,    29.4  V/    ffi     A  . 
Mean  pressure,  P=~ir» — _^  I  \IT~  •*• )'  m  P°unds  per  square  inch. 

The  work  done  by  the  atmospheric  pressure  in  compressing  the  air 
is  144x14.7  (^-^,  which,  subtracted  from  the  gross  work  of  com- 
pression, will  remain  the  mechanic  work. 

*-211&*F2WJ?-lW*-tfH 


Example  12.  Required  the  gross  work  of  compressing  %f=16  cubic 
feet  of  air  to      =  4  cubic  feet  ? 


WORK  OF  HEAT  IN  AIR.  133 

Gross  work,   k «=  4233.6 x  16 1 J3 -1\=  67737.6  foot-pounds. 

Of  this  work  k  =  2116.8  (16  -  4)  =  25401.6  foot-pounds  was  done  by 
the  atmospheric  pressure,  leaving  k  -  67737.6  -  25401.6  =  4233.6  foot- 
pounds of  mechanic  work  above  that  of  the  atmosphere. 

§  112.  WORK    OF    EXPANDING   AIR. 

V  and  ^  are  expressed  in  cubic  feet. 

K=  work  in  foot-pounds  done  of  expanding  V  cubic  feet  of  air  to  ^. 


*=  4233.6  V^l-^J 

The  work  done  against  the  atmospheric  pressure  will  be 

f-#).  15 


Subtract  Formula  14  from  15,  and  the  remainder  will  be  the  work 
done  in  expanding  the  air — namely, 

/       IW       \~l 

.    16 

The  following  tables  are  calculated  by  the  preceding  formulas,  as 
will  be  understood  by  the  headings.  The  works  K  and  k  mean  foot- 
pounds per  cubic  foot  of  the  primitive  volume  V,  expanded  or  com- 
pressed to  ^. 


134 


COMPRESSION  OF  AIR. 


TABLE   XXXI. 
% 

Compression  of  Air  by  External  Force. 

Volume. 

tr-L 

Temp. 
Fahr. 

Press 

Atmosp. 

stares.' 

ibs.  per  sq.  In. 

"Wo 

Gross. 

rks. 
Mechanic. 

t 

T 

A 

P 

K 

k 

1.00 

32. 

1.000 

14.7 

0. 

0. 

0.95 

41.7 

1.080 

15.9 

110.08 

4.19 

0.90 

52.3 

1.171 

17.2 

229.04 

17.36 

0.85 

63.7 

1.276 

18.7 

358.17 

40.60 

0.80 

76.3 

1.398 

20.5 

499.56 

76.20 

0.75 

90.5 

1.545 

22.7 

660.44 

131.19 

0.70 

105.2 

1.707 

25.1 

826.40 

191.36 

0.65 

122.1 

1.908 

28.0 

1077.4 

336.29 

0.60 

141.1 

2.151 

31.6 

1232.0 

385.28 

0.55 

162.7 

2.452 

36.0 

1475.0 

522.39 

0.50 

187.3 

2.828 

41.5 

1753.5 

694.60 

0.45 

216. 

3.313 

48.7 

2075.5 

910.71 

0.40 

250. 

3.953 

58.1 

2460.1 

1190.0 

0.35 

291. 

4.829 

71.0 

2922.4 

1546.4 

0.33 

306.5 

5.196 

76.4 

3095.2 

1684.0 

0.30 

341.1 

6.085 

89.4 

3495.7 

2014.0 

0.25 

407. 

8.000 

117.6 

4233.6 

2671.0 

0.20 

495.5 

11.18 

164.3 

5232.7 

3539.3 

0.15 

624.1 

17.15 

252.1 

6684.9 

4885.6 

0.125 

718. 

22.63 

322.7 

7740.7 

5888.5 

0.10 

843. 

31.63 

465. 

9157.3 

7252.2 

0.05 

1334 

89.44 

1315. 

14700 

12690 

0.04 

1532 

125. 

1837. 

16934 

14902 

0.03 

1822 

192. 

2828. 

20209 

18156 

0.02 

2309 

353.5 

5196. 

25703 

23629 

0.01 

3407 

1000 

14700. 

38102 

36006 

EXPANSION  OF  AIR. 


135 


TABLE   XXXIJ. 
Expansion  of  Air  by  External  Force. 

Volume. 

V-l. 

Temp. 
Fahr. 

3?res 

Atmosp. 

aiires. 
Ibs.  per  sq.  in. 

Wo 

Gross. 

rks. 
Mechanic. 

* 

T 

A 

P 

K' 

V 

1.0 

32 

1.0 

14.7 

0. 

0. 

1.1 

14.6 

0.8668 

12.74 

197.03 

14.65 

1.2 

-0.7 

0.7607 

11.18 

368.87 

54.49 

1.3 

-14.1 

0.6747 

9.918 

517.94 

117.1 

1.4 

-26.1 

0.6037 

8.874 

655.58 

119.1 

1.5 

-36.8 

0.5443 

8. 

776.86 

281.6 

1.6 

-46.5 

0.4941 

7.263 

886.64 

383.4 

1.7 

-54.4 

0.4512 

6.632 

986.60 

295.2 

1.8 

-63.5 

0.4141 

6.087 

1078.1 

615.3 

1.9 

-70.9 

0.3818 

5.612 

1162.3 

742.8 

2.0 

-77.8 

0.3535 

5.196 

1239.6 

877.2 

2.25 

-93.0 

0.2963 

4.355 

1411.2 

1235 

2.5 

-  105.8 

0.2530 

3.719 

1500.0 

1676 

2.75 

-116.9 

0.2193 

3.223 

1680.6 

2024 

3.0 

-  126.5 

0.1924 

2.828 

1789.7 

2444 

3.25 

-  135.0 

0.1707 

2.509 

1885.2 

2877 

3.50 

-  142.6 

0.1527 

2.244 

1970.6 

3322 

3.75 

-  149.3 

0.1377 

2.024 

2047.4 

3774 

4. 

-155.5 

0.1250 

1.837 

2116.8 

4234 

4.5 

-166.2 

0.1048 

1.540 

2237.8 

5171 

5. 

-175.3 

0.0894 

1.314 

2340.3 

6127 

6. 

-189.9 

0.0686 

1.008 

2505.4 

8084 

7. 

-  201.3 

0.0540 

0.793* 

2633.4 

10067  . 

8. 

-210.4 

0.0442 

0.650 

2736.8 

12080 

9. 

-218.0 

0.0370 

0.544 

-    2822.7 

14112 

10. 

-224.4 

0.0251 

0.369 

2894.8 

16157 

136 


PHYSICAL  PROPERTIES  OF  AIR. 


CARBONIC  ACID   AS  A  PERMANENT  GAS. 

§  113.  When  carbonic  acid  is  not  in  contact  with  its  liquid,  the 
relation  between  volume  and  pressure  behaves  like  that  of  a  per- 
manent gas,  and  its  ideal  zero  is  about  -  200  centigrade. 

The  latest  and  most  reliable  experiments  on  carbonic  acid  as  a  per- 
manent gas  have  been  made  by  Dr.  Andrews,  from  which  experi- 
ments the  following  formulas  are  deduced  both  in  centigrade  and 
Fahrenheit's  scales  of  temperature. 

^  =  volume  of  carbonic  acid  gas  of  temperature  T  centigrade,  and 
of  pressure  A  in  atmospheres,  compared  with  the  volume  at 
zero  centigrade  and  under  atmospheric  pressure. 

t  =  Fahrenheit  temperature,  and 

P  =  pressure  in  pounds  per  square  inch  above  vacuum. 


Volume, 

Temperature, 

Pressure, 


Formulas  for  Centigrade  Scale. 

,  =  1  |  T-IAA 
~A +    200J.    ' 

T=A  (200^-1.4)  -200. 
T-f  200 


A  = 


200-^  - 1.4* 


Volume, 
Temperature, 


Formulas  for  Fahrenheit  Scale. 

300  +t 


22.45P 
«  =  22.45/^-300. 


The  volume  corresponding  to  T  =  0  and  A  =  l,  formula  1,  should 
be  the  unit  1  instead  of  0.993  as  shown  in  the  table ;  but  the  course 
of  Dr.  Andrew's  experiments  indicate  that  the  primitive  volume  had 
probably  been  0.993.  The  error  is  only  0.007,  which  is  corrected  in 
formula  4. 


CARBONIC  ACID. 


137 


TABLE  XXXIII. 

Volume  of  Carbonic  Acid  Gas  of  Different  Temperatures 
and  Pressures. 


Tempei 
Fahr. 

•atures. 
Cent. 

l 

10 

Pressure  A  1 
20 

ii  Atmoftpher 
30 

•. 
40 

50 

t 

T 

if 

t 

t 

t 

t 

* 

32 

0 

0.993 

0.093 

0.0430 

0.02633 

0.01800 

0.013 

50 

10 

1.044 

0.098 

0.0455 

0.02800 

0.01925 

0.014 

68  ' 

20 

1.098 

0.103 

0.0480 

0.02966 

0.02050 

0.015 

86 

30 

1.148 

0.108 

0.0505 

0.03133 

0.02175 

0.016 

104 

40 

1.198 

0.113 

0.0530 

0.03300 

0.02300 

0.017 

120 

50 

1.248 

0.118 

0.0555 

0.03466 

0.02425 

0.018 

140 

60 

1.298 

0.123 

0.0580 

0.03633 

0.02550 

0.019 

158 

70 

1.348 

0.128 

0.0605 

0.03800 

0.02675 

0.020  • 

176 

80 

1.393 

0.133 

0.0630 

0.03966 

0.02800 

0.021 

'194 

90 

1.448 

0.138 

0.0655 

0.04133 

0.02925 

0.022 

212 

100 

1.498 

0.143 

0.0680 

0.03400 

0.03050 

0.023 

230 

110 

1.548 

0.148 

0.0705 

0.04466 

0.03175 

0.024 

248 

120 

1.598 

0.153 

0.0730 

0.04633 

0.03300 

0.025 

266 

130 

1.648 

0.158 

0.0755 

0.04800 

0.03425 

0.026 

284 

140 

1.698 

0.163 

0.0780 

0.04966 

0.03550 

0.027 

302 

150 

1.748 

0.168 

0.0805 

0.08050 

0.03675 

0.028 

CARBONIC  ACID  AS  A  VAPOR. 

§  114.  When  carbonic  acid  evaporates  from  or  condenses  to  liquid, 
the  relation  between  temperature  and  pressure  behaves  like  that  of  a 
vapor,  and  its  ideal  zero  is  at  about  -  260°  Fahr. 

The  yet  most  reliable  experiments  on  carbonic  acid  vapor  have 
been  made  by  Pelouze  and  Faraday,  from  which  experiments  the  fol- 
lowing formulas  and  table  are  deduced — namely, 

T= temperature  Fahrenheit  of  the  liquid  or  vapor  of  carbonic  acid. 

A  =  pressure  in  atmosphere. 

P=  pressure  in  pounds  per  square  inch  above  vacuum. 


Pressure  atmos.,     A  = 


(T+260)4 
208513600' 


Logarithm,        8.3191344. 


Pressure  Ibs., 


P= 


(T+260)4 


1421700 
Logarithm,         7.1527888. 


.     7 


.    8 


138 


PHYSICAL   PROPERTIES  OF  AIR. 


Temperature,          T- 120.1 7  y'Z  -  260. 
Temperature,          T  =  61.404]/  P-  260. 


.     9 
.  10 


It  appears  from  the  above  formulas  that  liquid  carbonic  acid  freezes 
to  solid  at  the  low  temperature  -  260°.  The  freezing  point  of  liquid 
carbonic  acid  is  variously  given  by  different  authors,  of  which  Olm- 
stead  says  -  85°,  but  Faraday  experimented  with  liquid  carbonic  acid 
at  --148°  without  it  freezing. 

TABLE  XXXIV. 
Carbonic  Acid  Vapor,  Pressure  and  Temperature. 


Fahr. 
Temp.  T. 

Press 
Aim.  A. 

ures. 
fcs.P. 

Fahr. 
Temp.  T. 

Pre 

Atm.^4 

ssures. 
fcs.  P. 

Fahr. 
Temp.  T 

Pres 
Amt.^4 

5ii  res. 
&s.P. 

-260 

0 

0 

-85 

4.5 

66.15 

88 

70 

1029 

-192 

0.1 

1.47 

-81 

5 

73.5 

99 

80 

1176 

-180 

0.2 

2.94 

-72 

6 

88.2 

110 

90 

1323 

-  171 

0.3 

4.41 

-65 

7 

102.9 

120 

100 

1470 

-164 

0.4 

5.88 

-58 

8 

117.6 

129 

110 

1617 

-159 

0.5 

7.35 

-52 

9 

132.3 

138 

120 

1764 

-154 

0.6 

8.82 

-47 

10 

147 

146 

130 

1911 

-150 

0.7 

10.29 

-36 

12 

176.4 

153 

140 

2058  ' 

-146 

0.8 

11.76 

-24 

15 

220.5 

160 

150 

2205 

-143 

0.9 

13.23 

-  6 

20 

294 

167 

160. 

2352 

-140 

1 

14.7 

+  9 

25 

267.5 

174 

170 

2499 

-127 

1.5 

22.05 

21 

30 

441 

180 

180 

2646 

-117 

2 

29.4 

32 

35 

514.5 

186 

190 

2789 

-109 

2.5 

36.75 

42 

40 

588 

192 

200 

2940 

-102 

3 

41.1 

51 

45 

661.5 

197 

210 

3087 

-  96 

3.5 

51.45 

59 

50 

735 

207 

220 

3234 

-  90 

4 

58.8 

74 

60 

882 

212 

238 

35  0 

PROPERTIES  OF  STEAM.  139 


STEAM  OK  AQUEOUS  VAPOR. 

§  115.  Water  under  atmospheric  pressure  evaporates  at  ordinary 
temperatures  un,der  the  boiling  point  ;  but  that  evaporation  takes 
place  only  on  the  surface  in  contact  with  the  air. 

When  the  temperature  of  the  water  is  elevated  to  or  above  that  of 
the  boiling  point,  then  evaporation  takes  place  in  any  part  of  the 
water  where  the  temperature  is  so  elevated. 

The  temperature  of  the  boiling  point  depends  upon  the  pressure  on 
the  surface  of  the  water. 

P=  pressure  in  pounds  per  square  inch  above  vacuum  on  the  sur- 

face of  the  water. 
T=  temperature  Fahr.  of  the  boiling  point. 

T=2001/Jr-101  ......    1 


Example  1.  At  wThat  temperature  will  water  boil  under  a  pressure 
of  P=8  pounds  to  the  square  inch? 

This  is  under  a  vacuum  of  14.7  -  8  =  6.7  pounds  to  the  square  inch. 

Temperature,          T=  2001/~8^  101  =  181.8°. 

Example  2.  What  pressure  is  required  to  elevate  the  temperature 
of  the  boiling  point  of  water  to  T=  330°  ? 

,    /  330°  +  101  Y 
Pressure,  P=(  -  -     =100  pounds. 

\       20°       / 

The  temperatifre  of  the  boiling  point  is  the  same  as  that  of  the  steam 
evaporated  under  the  same  pressure. 

Supposing  the  above  formulas  to  be  correct,  the  ideal  zero  of  aqueous 
vapor  should  be  at  -101°  Fahr.,  or  at  the  temperature  101°  below 
Fahr.  zero,  there  is  no  pressure  of  the  vapor  ;  that  is,  the  force  of 
attraction  between  the  atoms  is  equal  to  the  force  of  expansion  by 
heat. 

LATENT  HEAT  OF  STEAM. 

§  116.  One  pound  of  water  heated  under  atmospheric  pressure, 
from  32°  to  212°,  requires  180.9  units  of  heat.  If  more  heat  is  sup- 
plied, steam  will  be  generated  without  elevating  the  temperature  until 
all  the  water  is  evaporated,  which  requires  1146.6  units  of  heat,  and 


140  PHYSICAL  PROPERTIES  OF  AIR. 


the  steam  volume  will  be  1740  times  that  occupied  by  the  water  at 
32°.  Then,  1146.6-180.9  =  965.7  units  of  heat  in  the  steam  which 
have  not  increased  its  temperature.  This  is  what  is  called  latent  heat, 
because  it  does  not  show  as  temperature,  but  is  the  heat  consumed  in 
performing  the  work  -of  steam. 

One  cubic  foot  of  water  at  32°  weighs  6^387  pounds,  if  heated  to 
the  boiling  point  212°,  requires  62.387  x  180.9°  -  11285.8  units  of  heat, 
and  if  evaporated  to  steam  under  atmospheric  pressure,  requires 
62.387x1146.6^71532.9  units  of  heat,  of  which  71532.9-11285.8 
=  60247.1  will  be  latent.  It  is  this  latent  heat  which  generated  1740 
cubic  feet  of  steam  from  the  cubic  feet  of  water. 

The  work  accomplished  by  that  latent  unite  of  heat  against  the 
atmospheric  pressure  will  be 

K=  144  x  14.7  x  (1740  -  1)  =  3681115  foot-pounds. 

3681115 
Foot-pounds  per  unit  of  heat,         J  =  —  -  —  =  61.1. 


The  heat  expended  in  elevating  the  temperature  of  the  water  from 
32°  to  212°  is  not  realized  as  work. 


VOLUME  OF  WATER. 

§  117.  Water,  like  other  liquids,  expands  in  heating  and  contracts 
in  cooling,  with  the  exception  that  in  heating  it  from  32°  to  40°  it 
contracts,  and  expands  in  heating  from  40°  upwards.  The  greatest 
density  or  smallest  volume  of  water  is  therefore  at  40°  Fahr. 

The  most  reliable  experiments  made  on  this  subject  are  probably 
those  of  KOPP,  by  which  the  greatest  density  of  water  is  indicated  to 
be  between  39°  and  40°,  or  nearer  39°  ;  but  however  accurate  these 
experiments  might  have  been  made,  it  is  impossible  without  the  aid  of 
mathematics  to  determine  correctly  the  temperature  of  the  greatest 
density  because  the  curve  tangents  the  abcissa  at  that  point. 

The  writer  has  treated  Kopp's  experiments  with  very  careful  math- 
ematical and  graphical  analysis,  the  result  of  which  located  the  great- 
est density  of  water  at  40°. 

The  formula  for  volume  of  water  deduced  from  Kopp's  experi- 
ments is 

(t-40)* 


'=1 


1400  t  +  398500 


PROPERTIES  OF  WATER  AND  STEAM.  141 

The  volume  deduced  from  the  same  experiments,  but  with  the  as- 
sertion that  the  greatest  density  of  water  is  at  39°,  will  be 

(*-8»)' 


1 400  T+  405400 
The  Formula  1  is  the  most  correct. 

LATENT  AND  TOTAL  HEAT  IN  WATER  FROM  32°. 

§  118.  When  water  expands  it  absorbs  heat,  which  is  not  indicated 
i  temperature,  but  remains  latent. 
/  =  latent  heat  per  pound  of  water  heated  from  32°. 

V^  volume  per  Formula  1. 

t  =  temperature  of  the  water. 

h  =  total  units  of  heat  per  pound  of  water  heated  from  32°. 
•Latent  heat,  J-=0.1t(#-l) 3 

Total  heat,  A  =  0.1  t  (#+9) -32.          ...        4 


Cubic  Feet  per  Pound. 


e- 


62.388 


Pounds  per  Cubic  foot. 

=  62.388 

1 

"€'*'' 


is,  the  water  indicates  more  temperature  than  units  of  heat  imparted 
to  it.  The  volume  at  32°  is  1.000156,  and  the  heat  required  to  raise 
the  temperature  of  one  pound  of  water  from  32°  to  40°  or  88°  are 
0.999844  x  8  =  7.99875  units. 

The  heat  required  to  raise  the  temperature  of  one  pound  of  water 
from  32°  to  212°  or  180°  are  181  units.  The  heat  required  to  raise 
water  from  32°  to  350°  or  318°  are  322  units,  or  4  units  more  than 
the  increase  of  temperature. 

LATENT   AND    TOTAL    UNITS   OF    HEAT    IN    STEAM. 

§  119.  The  unit  of  heat  required  to  elevate  the  temperature  of  one 
pound  of  water  of  32°  to  the  boiling  point  and  evaporate  it  to  satu- 
rated steam  of  temperature  !F  is 

Units  of  heat,       #=1082  +  0.305  T.        ....        1 
Latent  heat,          L  =  1082 + 0.305  T  -  [0.1  T  ( #+  9)  -  32]. 

L  - 1114  T  (0.595  -0.1  V).  .        .  2 


142  PHYSICAL  PROPERTIES  OF  AIR. 

The  Formula  1  is  given  by  Regnault.  The  author  has  reason  to 
believe  that  the  formula  for  units  of  heat  in  steam  evaporated  from 
water  heated  from  32°  should  be 

per  cubic  foot  H'  =  2.8  P  =  2.8 


r    2.8  P     2.8  IT-  101  \« 
per  pound,        *-_-—  (-^--J 

The  latent  heat  in  steam  by  the  new  Formulas  3  and  4  should  be 
Per  cubic  foot,          L'  =  2.8  P-  ^  T.        ....        5 

9  &  P 
Per  pound,  £  =  —  —  -T    .....         6 

? 

This  includes  also  the  latent  heat  in  the  water  at  the  boiling  point, 
which  is  1  =  0.1  t(V-V). 

The  thermo-dynamic  equivalent  per  unit  of  latent  heat  will  be 


2.8  P-  f  T 

§  120.  The  combination  of  the  Regnault  formula  for  units  of  heat 
with  the  Fairbairn  formula  for  volume  of  steam  does  not  give  a  con- 
stant thermo-dynamic  equivalent  of  heat,  which  it  ought  to  do, 
and  therefore  either  or  both  the  formulas  are  defective.  The  arith- 
metical ratio  0.305  T  in  Regnault's  formula  cannot  be  correct,  for  the 
reason  that  the  pressure  increases  as  the  sixth  power  of  the  temper- 
ature, and  the  volume  decreases  nearly  as  the  cube  of  the  temperature. 

The  thermo-dynamic  equivalent  of  heat  in  saturated  steam  accord- 
ing to  Formula  3  will  be 

144  P 

J=  —  — •  =  51.5,  a  constant  number. 
2.8  P 

That  is  to  say,  one  or  each  unit  of  heat  in  saturated  steam  of  any  pres- 
sure, but  without  expansion,  generates  51.5  foot-pounds  of  work. 
This  equivalent,  multiplied  by  1+ hyperbolic  logarithm  for  expan- 
sion, gives  the  thermo-dynamic  equivalent,  which  can  be  realized  by 
steam-power. 

It  has  been  explained  (§  10)  that  the  steam-pressure  is  inversely  as 
the  expansion,  which  rule  is  sufficiently  correct  within  our  limit  of 
practice ;  but  when  the  temperature  of  aqueous  vapor  is  reduced  to 


SUPERHEATED  STEAM.  143 

the  ideal  zero — 101  Fahr. — its  pressure  will  be  0 ;  that  is,  the  expan- 
sive force  of  the  heat  is  equal  to  the  force  of  attraction  between  the 
atoms  of  the  vapor.  The  vapor  at  that  temperature  will  maintain  a 
constant  volume  without  being  enclosed  in  a  vessel. 

The  total  heat  per  pound  of  steam,  Formula  4,  is  nearly  constant 
for  all  pressures  and  temperatures,  differing  only  by  the  latent  heat  in 
the  water  heated  from  32°  to  the  boiling  point  under  the  pressure  P. 


DRYNESS   OR    HUMIDITY    OF   STEAM. 

§  121.  We  have  yet  no  reliable  means  by  which  to  determine  cor- 
rectly the  dryness  or  humidity  of  steam,  the  knowledge  of  which  is 
of  great  importance  in  steam  engineering. 

A  steam-engine  supplied  with  over-saturated  steam  does  not  trans- 
mit the  full  power  -due  to  the  consumption  of  fuel,  and  thus  the  rate 
of  evaporation  is  not  a  correct  measure  of  the  power  or  steaming  ca- 
pacity of  the  boiler. 

The  best  means  yet  at  our  disposal  by  which  to  measure  the  qual- 
ity of  the  steam  working  an  engine  is  to  compare  the  steam-volume 
passed  through  the  cylinder  with  that  due  to  the  water  evaporated  in 
the  same  time,  but  we  have  yet  no  reliable  data  as  to  the  volume  of 
steam  compared  with  that  of  its  water.  The  experiments  of  Fairbairn 
and  Tate  were  made  on  a  very  small  scale  and  by  apparatus  which 
did  not  admit  of  delicate  measurements,  and  operating  so  widely  dif- 
ferent from  that  of  a  steam-boiler  that  we  have  reason  to  doubt  the 
correctness  of  the  steam-volume  deduced  therefrom ;  nor  does  that 
volume  for  different  pressures  agree  with  the  law  of  expansion  of 
steam — namely,  that  the  volume  is  inversely  as  the  pressure. 

We  know  the  specific  gravity  of  steam  at  212°,  which,  compared 
with  that  of  water  at  32°,  makes  the  steam-volume  at  212°  =1730 
times  that  of  water  at  32°.  We  also  know  that  one  volume  of  water 
at  32°  resolved  into  its  elements,  oxygen  and  hydrogen,  gases  heated 
under  atmospheric  pressure  to  212°,  makes  2610.66  volumes  of  gas, 
of  which  there  are  870.22  volumes  of  oxygen  and  1740.44  volumes 
of  hydrogen. 

§  122.  When  the  elements  are  again  chemically  combined  from  gas 
to  vapor,  the  volume  of  hydrogen  takes  up  the  volume  of  oxygen, 
leaving  only  1740.44  volumes  of  vapor,  which  is  probably  the  correct 
volume  of  steam  at  212°.  If  the  volume  of  steam  increases  as  the 
pressure  increases,  the  steam  volume  at  any  pressure  would  simply  be 
^  =  25584.468  :  P;  but  the  decrease  of  volume  is  accompanied  with 
an  increase  of  temperature  which  expands  the  volume  in  the  same 


144 


STEAM  ENGINEERING. 


ratio  as  the  volume  of  water  is  increased  for  the  same  difference  of 
temperature. 

Call  the  volume  of  water  ^  1  at  40°,  then  for  any  other  temper- 
ature, according  to  Copp's  experiments,  the  volume  will  be 

(t-40)' 


1 400  t  +  398500 

At  212°   the  volume  of  water  is  1.0426.      Therefore  the  steam 
volume  at  any  pressure  and  temperature  should  be 

25584.468  /  (T-40)2       \ 

1.0426  P  \       1400  T+  398500  / 

The  temperature  of  water  and  steam  being  alike,  the 

24539  # 

Steam  volume,         y  =  —      — .          ....     3 
P 


TABLE  XXXV. 

Comparison  of  Volume  and  Temperature  of  Steam  at 
Different  Pressures. 


Steam  -pres- 
sure. 

Volume  ( 
Fairbairn. 

f  Steam. 
Nystrom. 

Temperatui 
Begnault. 

e  of  Steam. 
Nystrom. 

14.7 

1641.5 

1740 

212° 

212° 

25 

984.23 

1035 

240.07 

241.0 

50 

508.29 

527.2 

280.89 

282.8 

75 

348.15 

355.8 

307.42 

309.8 

100 

267.80 

269.4 

327.6 

329.9 

150 

187.26 

181.8 

358.4 

360.0 

200 

146.93 

138 

381.8 

382.6 

300 

106.54 

94.22 

417.7 

416.5 

400 

86.33 

71.19 

445.1 

441.9 

Comparison  of  Fairbairn's   experiments   and   formulas   with   the 
author's  steam  volume : 


By  Fairbairn's  formula 

By  Fairbairn's  experiment 
By  the  author's  formula.... 


Pres.  P=  60.6 
^  =  428 
^  =  432 
^=437 


Pres.  P=8 


=  3046 
=  3150 


Pres.  P=  4.7 
^  =  4900 
^  =  4914 
^  =  5336 


PROPERTIES  OF  WATER  AND  STEAM.  145 


The  Regnault  experiments  on  temperature  and  pressure  of  steam 
gave  widely  different  results,  of  which  an  average  was  adopted,  and  it 
was  attempted  to  set  up  a  formula  to  follow  the  average  curve,  which 
was  found  impossible,  for  which  reason  different  formulas  were  set  up 
for  different  parts  of  the  irregular  curve. 

The  formula  herein  adopted  gives  a  regular  curve  which  sweeps 
the  whole  range  of  the  Reguault  experiments,  and  it  coincides  in 
several  places  with  the  irregular  or  average  curve. 

The  volume  of  one  pound  of  steam  in  cubic  feet  will  be 

393.333  ff 
P 

The  steam  volume  formula  by  Fairbairn  and  Tate  is 

•     *— fH « 

/=  inches  of  mercury.  That  is  to  say,  the  steam  volume  cannot  be 
reduced  below  25.62. 

For  very  high  pressures  we  can  omit  the  fraction  0.72  and  insert 
2.0372  P  for  J— namely, 


When  the  steam-pressure  is  P=  24304  pounds  to  the  square  inch, 
the  volume  should  be  26.62. 

The  temperature  corresponding  to  this  pressure  is 

T  =  200 V6/  24304  -101=  975°  Fahr.         .         .     6 
The  volume  of  water  at  this  temperature  will  be 

*;_]  +       (975-40)'         i64  7 

1400x975.+ 398500 

Then  26.62  - 1.64  =  25  volumes,  of  steam  pressure  P=  24304,  which 
cannot  be  materallly  reduced  by  additional  pressure,  because  an  in- 
crease of  pressure,  would  only  affect  the  decimals  of  that  volume.  The 
reason  why  the  water  volume  is  subtracted  from  that  of  the  steam,  is 
that  the  water  volume  is  considered  to  be  the  limit  to  which  that  of 
steam  can  be  reduced. 

It  will  be  noticed  that  Fairbairn's  experimental  numbers,  24304 
and  25.62,  agree  nearly  with  the  writer's  numbers,  24539  and  25, 
which  fact  deserves  consideration. 

10 


146  STEAM  ENGINEERING. 

Messrs.  Fairbairn  and  Tate  omitted  the  consideration  of  expansion 
of  water,  for  which  reason  they  were  obliged  to  add  the  empirical 
constant  25.62  in  their  formula. 

The  above  argument  proves  conclusively  that  the  steam  volume 
experiments,  as  well  as  the  formula  of  Fairbairn  and  Tate,  cannot  be 
relied  upon,  and  they  do  not  agree  with  the  law  of  expansion  of 
vapors. 

The  object  of  this  paragraph  is  to  determine  the  dryness  or  humid- 
ity of  steam,  for  which  purpose  the  volume  due  to  the  evaporation 
should  be  compared  with  the  volume  of  steam  passing  through  the 
steam  cylinder. 

W=  cubic  feet  of  water  at  32°,  evaporated  during  ^/"revolutions  of 

the  engine. 

^  =  Steam  volume  compared  with  that  of  its  water  at  32°. 
Q  =  cubic  feet  of  steam  passing  through  the  engine  or  cylinder  at 

each  revolution  or  double  stroke  of  the  piston. 
N=  total  number  of  revolutions  of  the  engine  in  the  time  W  cubic 

feet  of  water  is  evaporated. 
%  =  per  centage  of  water  in  the  steam. 
V=  volume  of  water  at  the  temperature  of  the  steam. 


The  steam-piston  and  valves  must  be  perfectly  tight,  and  the  capa- 
city of  the  steam-ports  and  clearance  of  piston  must  be  included  in  Q. 
§  123.  In  the  ordinary  engine  the  admittance  of  steam  is  generally 
cut  off  before  the  piston  has  reached  the  end  of  the  stroke,  in  which 
case  the  steam  volume  Q  must  be  determined  from  the  indicator 
diagram,  as  follows : 

Measure  the  steam-pressure  p  on  the  diagram  where  the  expansion 

curve  begins  to  be  reg- 
ular. The  steam  volume 
Tfr  corresponding  to  this 
pressure  must  be  used  in 
the  formula.  Measure  the 
distance  Q  in  feet,  which, 
multiplied  by  the  area  of 
the  piston  in  square  feet, 
is  the  cubic  capacity  of 
the  steam,  to  which  add 
the  capacity  of  the  clear- 


SUPERHEATED  STEAM.  147 

ance  and  steamport,  and  the  sura  is  Q.  This  measurement  must  be 
made  for  both  sides  of  the  piston. 

The  steam-pressure  should  be  kept  as  constant  as  possible  during 
the  experiment ;  but  in  a  long  run  it  is  difficult,  if  not  impossible,  to 
keep  it  stationary,  for  which  a  mean-pressure  must  be  determined,  as 
follows  : 

The  expansion  being  constant  during  the  operation  and  the  steam- 
pressure  by  gauge,  noted  at  short  and  regular  intervals  of  time,  and 
the  mean-pressure  represented  byjo". 

p'  —  steam-pressure  by  gauge  at  the  time  the  pressure  p  is  taken 

on  the  diagram. 
p'"  =  mean-pressure  for  the  volume  ^  in  the  formula. 

p"'  :  p"  =p'  :  p         and        p'"  —*-*—. 

P 

Small  steam-engines  ought  to  be  constructed  for  the  purpose 
of  measuring  the  volume,  dryness  or  humidity  of  steam.  The  slide 
valve  in  such  an  engine  should  have  no  lap  or  lead  on  the  steam  and 
exhaust  ports,  so  that  the  full  capacity  of  the  cylinder,  including  clear- 
ance and  steamport,  would  be  the  correct  measure  of  the  steam  volume 
for  each  stroke.  The  cylinder  and  short  steam-pipe  could  be  well 
covered  with  felt,  so  that  the  pressure  in  the  boiler  would  correspond 
to  the  volume  ^  in  the  engine. 

The  exhaust  steam  could  be  condensed  in  a  surface  condenser  and 
the  water  measured  independent  of  the  evaporation  in  the  boiler. 
Such  an  engine  could  be  temporarily  attached  to  any  boiler  for  the 
purpose  of  testing  its  quality  of  steam,  and  the  properties  of  super- 
heated steam,  which  are  yet  not  well  understood. 


SUPERHEATING    STEAM. 

§  124.  When  steam  is  superheated  after  generated  in  the  wrater, 
the  relation  between  temperature  and  pressure  will  remain  the  same 
as  if  the  same  steam  had  been  evaporated  at  the  same  temperature  as 
that  to  which  it  is  superheated  as  long  as  it  is  in  contact  with  the 
water.  When  steam  is  shut  off  from  the  water  from  which  it  is  gen- 
erated and  then  superheated,  the  relation  between  temperature  and 
pressure  will  still  remain  the  same  as  for  saturated  steam,  provided 
the  volume  is  not  increased  to  or  over  50  per  cent. 

When  steam  is  superheated  above  the  temperature  and  pressure 
due  to  saturated  steam,  and  the  volume  is  increased,  the  hydrogen  is  not 


148  STEAM  ENGINEERING. 

capable  of  holding  all  the  oxygen  in  its  own  volume ;  but  part  of  the 
vapor  is  converted  into  gas  until  the  volume  is  increased  50  per  cent., 
when  all  the  vapor  is  converted  into  gas.  For  instance,  if  four  cubic 
feet  of  steam  is  superheated  under  constant  pressure  until  its  volume 
becomes  six  or  more  cubic  feet,  that  volume  will  then  not  be  vapor 
but  a  gas  which  maybe  exploded  by  ignition  (?)  In  the  ordinary 
use  of  steam  it  is  never  so  superheated,  but  is  always  in  contact  with 
water  which  prevents  its  conversion  into  gas,  and  it  requires  a  tem- 
perature above  ignition  about  600°  to  ignite  it  to  explosion. 

When  the  steam  is  superheated  to  gas  it  obeys  the  formulas  for  per- 
manent gases  already  explained. 

When  steam  is  passed  through  and  allowed  to  expand  in  iron  tubes 
heated  to  a  dull  red  heat,  say  800°,  the  steam  is  resolved  into  its 
elements,  the  oxygen  being  taken  up  by  the  hot  iron  and  the  hydro- 
gen gas  passing  off  without  explosion. 

A  definite  volume  of  saturated  steam,  superheated  in  a  closed 
vessel  without  water,  will  obey  the  formula 

T=  200|/T- 101, 

until  the  primitive  pressure  is  increased  50  per  cent.,  when  the  steam 
becomes  a  gas  and  obeys  the  formulas  for  permanent  gases  above  that 
pressure  and  temperature ;  but  being  enclosed  in  a  vessel  the  volume 
remains  constant. 

For  instance,  a  volume  of  steam  of  pressure  P  =  40  pounds  to  the 
square  inch,  which  corresponds  to  a  temperature  of 

T  =  200^40  - 101  -  268.87°, 

is  superheated  under  constant  volume  until  the  pressure  becomes 
P-  60,  the  temperature  will  be 

!F=  200^60  -  101  =  294.7°  ; 

the  steam  is  then  a  gas  of  f  volumes  of  hydrogen  and  ^  of  oxygen. 

W=  weight  in  pounds  of  the  saturated  steam  superheated. 

The  specific  heat  of  steam  gas  at  32°  under  atmospheric  pressure  is 
3.3  +  0.23  =  3.53. 

The  units  of  heat  h  required  to  superheat  W  pounds  of  saturated 
steam  of  pressure  p  and  temperature  t  to  pressure  P  and  temperature 
T  will  be 


SUPERHEATED  STEAM.  149 

P  and  p  both  mean  absolute  pressures  above  vacuum,  and  the  super- 
he atinir  accomplished  without  the  steam  being  in  contact  with  water. 
#=  volume  of  the  saturated  steam  of  pressure  p. 
tf  =  volume  of  the  superheated  steam  of  pressure  P. 
The  saturated  steam  becomes  a  perfect  gas  when  superheated  so  that 

V         ir  1.5  p     IT 

-,   or  when =  — 

P     1.5V  P        V 

Example.  How  many  units  of  heat  are  required  to  superheat 
W=  3  pounds  of  saturated  steam  of  pressure  p  =  40  and  temperature 
t  =  268.87°  to  a  perfect  gas  of  pressure  P=60  and  temperature 
T=  294.7°? 

Units  of  heat  h  =  3.53  x  3  J—  (294.7  -  268.87)  =  223.34. 

'  OU 

The  same  weight -of  steam  raised  from  p  =  4Q  to  P=60  of  satu- 
rated steam  would  require  -only  28  units  of  heat,  but  the  steam-vol- 
ume which  is  constant  in  the  preceding  example  would  in  this  latter 
case  be  one-third  less.  Then  223  -  28  =  195  units  of  heat  expended  in 
converting  the  vapor  into  gas  and  in  expanding  the  volume  50  per 
cent. 

It  would  therefore  appear  that  there  is  no  gain,  but  rather  a  loss,  in 
superheating  steam  without  contact  with  water  for  motive-power. 

The  expansive  property  of  vapor  generates  much  more  power  than 
does  that  of  steam-gas.  But  when  steam  is  to  a  limited  extent  super- 
heated in  contact  with  water,  the  expansive  property  is  not  impaired, 
and  the  water  which  may  be  carried  along  with  the  steam,  is  evaporated 
by  the  superheating ;  and  thus  there  is  a  considerable  gain  by  super- 
heating steam,  particularly  when  the  superheating  is  done  by  the  gases 
of  combustion  after  having  passed  the  water-seating  surfaces.  Steam- 
gas  is  very  injurious  to  the  sides  and  packing-rings  in  the  cylinder;  it 
creates  more  friction  and  is  more  difficult  to  condense  than  steam-vapor. 

NEW   TABLES   FOR   WATER    AND   STEAM. 

§  125.  The  following  tables  of  properties  of  water  and  steam  have 
been  calculated  by  the  preceding  new  formulas,  which  are  considered 
more  correct  than  the  old  ones.  The  meaning  of  each  column  is  ex- 
plained in  its  heading. 

In  the  first  two  water-tables  the  pressure  of  the  vapor  in  pounds 
per  square  inch  is  contained  in  the  last  column,  of  which  +  P  denotes 
the  absolute  pressure  above  vacuum,  and-p  the  pressure  under  that 
of  the  atmosphere,  which  is  the  vacuum. 


150 


TABLE  XXXVI.— Properties  of  Water. 


Tempe 
Centig. 

rat  ore. 
Fahr. 

Volume. 
Wat.  =  1  at 
40°. 

Weight 
>er  cubic 
foot. 

Bulk, 
cubic  feet 
per  Ib. 

Units  o 
perlb. 

f  beat, 
pr.  c.  ft. 

Pressure 
Absol. 

of  vapor, 
under  at. 

t 

0. 
0.55 
1.11 
1.66 
2.22 

T 

32 
33 
34 
35 
36 

v  . 

1.000109 
1.000077 
1.000055 
1.000035 
1.000020 
1.000009 
1.000003 
1.000001 
1.000000 
1.0001)03 

? 
62.3871 
62.3830 
62.3842 
62.3859 
62.3868 

G 

0.0160304 
0.0160299 
0.0160295 
0.0160292 
0.0160290 

h. 

0.00000 
1.00000 
2.00000 
3.00001 
4.00003 

h'. 

0.0000 
62.383 
124.77 
187.16 
249.55 

+  P. 

0.0864 
0.0904 
0.0946 

0.0988 
O.HKJ:; 

—  P- 

-14.614 
-14.610 
-14.606 
-14.601 
-14.597 

2.77 
3.33 
3.88 
4.44 
5.00 
5.55 
6.11 
6.66 
7.22 
7.77 

37 
38 
39 
40 
41 

62.3875 
62.3876 
62.3879 

r,L'.:;sso 
62.3878 

0."tll<iti2S8 
0.0160288 
0.0160287 
0.0160287 
0.0160288 

5.00006 

6.00010 
7.00015 
8.00022 
9.00030 
lo.ooo.ln 
11.00051 
12.00065 
13.00081 
14.00098 
15.00132 
16.00140 
17.00165 
18.00192 
19.00222 
20.00255 
21.00292 
22.00329 
23.00370 
24.00415 

311.99 
374.33 
436.72 
499.12 
561.51 

U.107!) 

0.1127 
0.1176 
0.1228 
0.1281 

-14I5D2 

-14.587 
-14.582 
-14.577 
-14.571 

42 
43 
44 
45 
46 

l.ooonit; 
1.000034 
1.000053 
1.000077 
1.000101 

62.3873 
62.3859 
62.3847 
62.3832 
62.3815 
"62:3797" 
62.3774 
62.3749 
62.3722 
62.3692 

(Mil  60290 
0.0160292 
0.0160295 
0.0160299 
0.0160304 

(J23.S9 
686.28 
748.66 
811.03 
879.40 
935.70 
997.77 
1060.0 
1122.8 
1185.1 

0.1336 

O.i:  :;<.):! 
0.1452 
0.1513 

0.1570 

-14.566 
-14.561 
-14.555 
-14.549 
-14.542 

8.33 
8.88 
9.44 
10.00 
10.55 

47 

48 
49 
50 
51 

1.000136 
1.000171 
1.000211 
1.000254 
1.000302 

0.0100308 
0.0160314 
0.0160321 
0.0160328 
0.0160335 

0.1642 

0.1709 
0.1780 
0.1852 
0.1927 

-14.536 

-14.529 
-14.522 
-14.515 
1  1.5D7 
1  I.I  '.ill 
-14.41)1 
-14.483 
-14.475 
-14.466 

11.11 
11.66 
12.22 
12.77 
13.33 

52 
53 
54 
55 
56 

1.000353 
1.000408 
1.000468 
1.000531 
1.000597 

62.3660 
62.3626 
62.3589 
62.3549 
62.3508 

O.OK.0344 
0.0160352 
0.0160362 
0.0160372 
0.0160383 

1248.0 
1310.1 
1372.3 
1434.3 
1496.4 

0.2004 
0.2084 
0.2166 
0.2252 
0.2339 

13.88 
14.44 
15.00 
15.55 
16.11 
16.66 
17.22 
17.77 
18.33 
18.88 

57 

58 
59 
60 
61 

l.l)l)li(iliS 

1.000740 
1.000819 
1.000901 
1.000986 

62.3464 
62.3419 
62.3370 
62.3319 
62.3266 

0.0160394 
0.0160405 
0.0160-118 
0.0160431 
0.0160445 

25.00462 
26.00513 
27.00568 
28.00626 
29.00687 

155s.fi 
1620.9 
1683.2 
1745.5 

1S07.S 

0.2430 
0.2524 
0.2621 
0.2720 
0.2824 

-14.457 
-14.448 
-14.438 
-14.428 
-14.418 

62 
63 
64 
65 
66 

1.001075 
1.001167 
1.001262 
1.001362 
1.001464 

62.3211 
62.3153 
62.3094 
62.3032 
62.2968 

0.0160459 
0.0160474 
0.0160489 
0.0160505 
0.0160522 

30.00752 
31.00821 
32.00894 
33.00970 
34.01051 

1S70.1 
1932.4 
1994.4 
2056.6 
2118.7 

0.2930 
0.3040 
0.3153 
0.3269 

n.:;;;s;i 

-14.407 
-14.396 
-14.385 
-14.373 
-14.361 

19.44 
20.00 
20.55 
21.11 
21.66 

67 

68 
69 
70 
71 

1.001570 
1.001680 
1.001793 
1.001909 
1.002028 

62.2902 
62.2834 
62.2763 
62.2692 
68.2618 

0.0160539 
0.0160556 
0.0160575 
0.0160592 
0.0160612 

35.01136 
36.01224 
37.01377 
38.01415 
39.01516 

2180.8 
2242.9 
2305.0 
2367.1 
2429.2 

o.::5i3 

0.3640 
0.3771 
0.3906 
0.4045 

-14.349 
-u.3:;6 
-14.323 
-14.309 
-14.296 

22.22 
22.77 
23.33 
23.88 
24.44 

72 
73 
74 
75 
76 

1.002151 
1.002277 
1.002406 
1.002539 
1.002675 

62.2541 
62.2463 
62.2383 
62.2300 
62.2216 
i>2.2  i:;o" 
62.2042 
62.1952 
62.1860 
62.1766 

0.0160632 
0.0160652 
0.0160673 
0.0160694 
0.0160716 

40.01622 
41.01733 
42.01848 
43.01968 
44.02092 
45.02222 
46.02356 
47.02495 
48.02640 
49.02789 

2491.2 
2553.2 
2615.2 
2677.1 
2739.2 

0.418S 
0.4336 
0.4487 
0.4644 
0.4804 

-14.281 
-14.266 
-14.251 
-14.236 

-1  I.L'L'I) 

25.00 
25.55 
26.11 
26.66 
27.22 

77 
78 
79 
80 
81 

1.002814 
1.002956 
1.003101 
1.003249 

1.003400 

0.0160738 
0.0160761 
0.0160784 
0.0160808 
0.0160832 

2S01.0 
2862.8 
2924.6 
2985.4 
3048.2 

0.4970 
0.5139 
0.5314 
0.5493 
0.5677 

-14.203 
-14.186 
-14.169 
-14.151 
-14.132 

27.77 
28.33 
28.88- 
29.44 
30.00 
30.55 
31.11 
31.66 

82 
83 
84 
85 

86 
87 
88 
89 

1.003554 
1.003711 
1.003872 
1.004035 
1.004199 
1.004370 
1.004542 
1.004717 

62.1671 
62.1574 
62.1474 
62.1373 
62.1272 
62.1166 
62.1059 
62.0951 

0.0160857 
0.0160882 
0.0160908 
0.0160934 
0.0160960 
0.0160987 
0.0161015 
0.0161043 

50.02944 
51.03104 
52.03269 
53.03439 
54.03615 
55.03797 
56.03984 
57.04177 

3111.0 
3172.8 
3234.4 
3296.2 
3358.2 
3418.7 
34S0.4 
3542.1 

o.5sos 
0.6063 
0.6264 
0.6470 
0.6681 
0.6898 
0.7121 
0.7351 

-14.113 

-14.093 
-14.074 
-14.053 
-14.032 
-14.010 
-13.988 
-13.965 

TABLE  XXXVII.— Properties  of  Water. 


151 


Tempei 
Cen.ig. 

•aturc. 
Fahr. 

Bulk, 
cub.  per  Ib. 

Units  o 
perlb. 

f  heat, 
pr.  c.  ft. 

Pressure 
Absol. 

of  vapor, 
under  at. 

Wat.  =  1  at 
40°. 

>er  cubic 
foot. 

t 

32.22 
32.77 
33.33 
33.88 
34.44 
35.00 
35.55 
36.11 
36.66 
37.22 

T 

90 
91 
92 
93 
94 

V 

.004894 
.005094 
.005258 
.005444 
.005633 

f 

62.0840 
62.0718 
62.0617 
62.0502 

62.03S6 

G 

0.016107 
0.016110 
0.016113 
0.016116 
0.016119 

h. 

58.0437 
59.0458 
60.0479 
61.0501 
62.0523 

h'. 

3603.8 
3665.0 
3726.6 
3788.2 
3849.8 

+  P. 
0.7586 
0.7827 
0.8075 
0.8329 
0.8590 

—  P- 

-13.94 
-13.91 
-13.89 
-13.86 
-13.84 

95 

96 
97 
98 
99 

1.005825 
.006019 
.006216 
.006415 
.006618 

Ol'.  (12(17 
62.0148 
62.0026 
61.9904 
61.9779 

0.016122 
0.016125 
0.016128 
0.016131 
0.016135 

63.0546 
64.0569 
65.0593 
66.0618 
67.0643 

3911.2 

3972.6 
4033.9 
4095.2 
4156.5 

O.SS5K 
0.9132 
0.9609 
0.9704 
1.000 

—13.81 
-13.79 
-13.74 
-13.73 
—13.70 

37.77 
38.33 
38.88 
39.44 
40.00 

100 
101 
102 
103 
104 

.006*22 
.007030 
.007240 
.007553 
.007668 

61.9653 
61.9525 
61.9396 
61.9204 
61.9133 

0.016138 
0.016141 
0.016145 
0.016150 
0.016152 
0.016155  ~ 
0.016159 
0.016162 
0.016166 
0.016169 

68.0669 
69.0696 
70.0723 
71.0751 
72.0779 

4217.7 

4278.9 
4340.1 
4401.3 
4462.5 
4523.0 
4585.0 
4645.9 
4706.8 
4767.7 

1.030 
1.061 
1.093 
1.126 
1.159 
1.194 
1.229 
1.265 
1.302 
1.340 

-13.67 
-13.64 
-13.61 
-13.57 
-13.54 

40.55 
41.11 

41.66 
42.22 

,  42.77 

105 
106 
107 
108 
109 

.007905 
.008106 
.008.328 
.008554 
.008781 

61.8987 
61.8864 
61.8728 
61.8589 
61.8450 

73.0809 
74.0838 
75.0869 
76.0900 
77.0932 
78.0965 
79.0998 
80.1032 
81.1067 
82.1103 

—13.50 
—13.47 
-13.43 
-13.40 
—13.36 

43.33 
43.88 
44.44 
45.00 
45.55 

110 
111 
112 
113 
114 
~~il5" 
116 
117 
118 
119 

.0()«!U32 
.009244 
.009479 
.009718 

1.009956 

61.8296 
61.8166 
61.8022 
61.7876 
61.7730 

0.016173 
0.016177 
0.016180 
0.016184 
0.016188 
0.016192 
0.016196 
0.016200 
0.016204 
0.016208 

4828.6 
4889.5 
4950.4 
5011.3 
5072.2 

1.378 
1.418 
1.459 
1.500 
1.543 

—13.32 
-13.28 
-13.24 
-13.20 
-13.16 

46.11 
46.66 
47.22 

47.77 
48.33 

1.010197 
1.010442 
1.010688 
1.010938 
1.011189 

61.7583 
61.74:53 
61.7283 
61.7130 
61.6977 

83.1139 
84.1176 
85.1214 
86.1252 
87.1292 

r>i  33.0 
5193.7 
5254.3 
5314.9 
5375.5 

1.587 
1.631 
1.677 
1.723 
1.771 

-13.11 
-13.07 
-13.02 
-12.98 
-12.93 

48.88 
49.44 
50.00 
50.55 
51.11 

120 
121 
122 
123 

124 

1.011442 
1.011698 
1.011956 
1.012216 
1.012478 

61.6823 
61.6666 
61.6509 
61.6351 
61.6192 

0.016212 
0.016216 
0.016220 
0.016224 
0.016229 

88.1332 
89.1373 
90.1414 
91.1456 
92.1500 

5436.1 
5496.6 
5557.1 
5617.6 
5678.1 

1.820 
1.870 
1.921 
1.974 
2.026 

-12.88 
-12.83 
-12.78 
-12.73 
-12.67 

51.66 

52.22 
52.77 
53.33 
53.88 

125 
126 
127 
128 
129 

1.012743 
1.013010 
1.013278 
1.013550 
1.013823 

61.6030 
61.5868 
61.5805 
61.5540 
61.5374 
61.5207 
61.4355 
61.3473 
61.2567 
(J1.16:',5 

0.016233 
0.016237 
0.016241 
0.016246 
0.016250 

93.1543 
94.1588 
95.1634 
96.1680 
97.1727 

5738.6 
5798.9 
5859.2 
5919.5 
5979.7 

2.082 
2.137 
2.195 
2.253 
2.312 
2.374 
2.699 
3.058 
3.462 
3.907 

-12.62 
-12.56 
-12.50 
-12.45 
-12.39 

54.44 
57.22 
60.00 

62.77 
65.55 

130 
135 
140 
145 
150 

1.014098 
1.015505 
1.016962 
1.018468 
1.020021 

0.016255 
0.016277 
0.016301 
0.016325 
0.016350 

98.1775 
103.2027 
108.230 
113.260 
118.291 
123.326 
128.362 
133.401 
138.443 
143.487 

6040.0 
6340.3 
6639.6 
6937.9 
7215.1 

-12.33 
-12.00 
-11.64 
-11.24 
-10.79 

(i8.33 
71.11 
73.88 
76.66 
79.44 

155 
160 

165 
170 
175 

1.021619 

.023262 
.024947 
.026672 
1.028438 

61.0678 
60.9697 
60.8695 
60.7673 
60.6620 

0.016375 
0.016401 
0.016429 
0.016456 
0.016485 
"  0.016513 
0.016543 
0.016573 
0.016604 
0.016635 
0.016667 
0.016799 
0.016811 

7531.2 

7826.2 
8098.1 
8412.8 
8704.2 

4.397 
4.939 
5.534 
6.188 
6.906 

-10.30 
-9.761 
-9.166 
-8.512 
-7.794 

82.22 
85.00 
87.77 
90.55 
93.33 
96.11 
98.88 
100.00 

180 
185 
190 

1  (.l.'> 

200 
205 
210 
212 

.n:;ir_>i2 
.032083 
.033960 
.035873 
1.037819 
.039798 
.041809 
.042622 

60.5567 

60.4487 
60.3389 
60.2275 
60.1146 
60.0002 
59.8843 
59.8376 

148.537 
153.583 
158.635 
163.691 
168.749 
173.809 
178.873 
180.900 

8994. 
9281. 
9571. 

9858. 
10318. 
10428. 
10712. 
18824. 

7.693 
8.550 
9.488 
10.51  • 
11.62 
12.83 
14.13 
14.70 

-  7.007 
-6.150 
-5.212 
-4.19 
-3.08 
-1.87 
-0.57 
0.000 

152 


PROPERTIES  OF   WATER. 


TABLE  XXXVIII. 

Water. 

TVmpe 
of  the 
Cent. 

rat  ure 
water. 

Fahr. 

~~T~ 

212. 
213. 

Volume, 
water  = 
1  at  40°. 

Weight. 
Ibs.  per 
cubic  ft. 

Bulk. 

i-iil.ir  i.-<-t 
per  pound. 

Units  of  h 
Tots 
pound. 

eat  in  wate 
1  per 
cubic  foot, 

r  from  31 
La  ten 
pound. 

10  to  T. 

tper 
cubic  ft. 

100. 
100.5 

V 
.04262 
1.04296 

? 
59.838 
59.819 

e 

0.01671 
0.01671 

h. 

180.90 
181.91 

h'. 

10825 
10882 

L 

0.903 
0.915 

t. 
54.03 
54.73 

102.4 

216.4 

1.04436 

59.743 

0.01674 

185.36 

11063 

0.957 

56.73 

104.2 
106. 
107.6 

219.6 
222.8 
225.7 

1.04534 
.04638 
1.04785 

59.668 
59.594 
59.520 

0.01676 
0.01678 
0.01680 

188.59 
191.83 
194.78 

11241 
11414 
11583 

0.994 
1.033 
1.082 

59.31 
61.56 

04.40 

109.1 
110.6 

22H.r> 
231.2 

1.041)4(5 
1.05062 

59.447 
59.384 

0.01682 
0.01684 

197.63 
200.37 

11749 
11895 

1.130 

1.170 

67.17 
69.48 

112.1 

233.8 

1.05175 

59.322 

0.01685 

203.01 

12037 

1.209 

71.72 

113.6 
114.8 

236.3 

238.7 

~24~UT 
243.3 

1.05284 
1.05389 

1.05490 
1.05588 

59.261 
59.201 

59.142 
59.086 

0.01687 
0.01689 

205.55 
207.98 

12175 
12309 

1.248 
1.281 

73.96 
75.71 

^8J9" 
80.38 

116.1 

117.7 

0.01690 
0.01692 

210.32 
212.66 

12439 
12561 

1.322 
1.359 

118.5 
119.7 
120.7 
T2UT 
123.0 

245.4 
247.5 
249.4 

1.05683 
1.05776 
1.05867 

59.032    0.01694 
58.980    0.01695 
58.930    0.01697 

214.79 
216.84 
218.86 

220.90 
222.93 

12678 
12791 
12901 

1.394 
1.437 
1.462 

82.42 
84.42 
86.32 

251.4 
253.4 

1.05955 
1.06042 

58.881 
58.832 

0.01698 
0.01700 

13007 
13113 

1.496 
1.532 

88.09 
90.02 

124.0 

255.3 

1.06128 

58.784 

0.01701 

224.86 

13217 

1.565 

91.92 

125.1 
126.1 

257.2 
259.0 

1.05213 

1.06297 

58.737 
58.690 

58.646 
58.603 

0.01702 
0.01704 

226.80 
228.63 

13318 
13416 

1.598 
1.630 

93.78 
95.65 

127.0 
128.0 

260.7 
262.4 

1.06380 
1.06460 

0.01705 
0.01706 

230.36 

232.09 

13510 
13602 

1.664 
1.695 

H7..V.) 
99.37 

128.9 

264.1 

1.06538 

58.561 

0.01707 

233.83 

13692 

1.726 

101.1 

129.8 
130.7 

265.7 
267.3 

1.06614 
1.06689 

58.519 

58.477 

0.01709 
0.01710 

235.45 
237.09 

13780 
13866 

1.756 
1.790 

102.8 
104.5 

131.6 
132.5 

268.9 
270.4 

1.06761 
1.06832 

58.437 
58.398 

0.01711 
0.01712 

238.72 
240.25 

13950 
14036 

1.816 
1.846 

106.1 
107.9 

133.4 

271.9 

1.06902 

58.359 

0.01713 

241.78 

14115 

1.879 

109.6 

134.0 
134.9 

273.3 

274.8 

1.06971 
1.07039 

58.321 

58.284 

0.01714 
0.01716 

243.20 
244.73 

14192 
14267 

1.905 
1.935 

111.2 
112.7 

135.6 
136.4 

276.2 
277.6 

1.07105 
1.07170 

58.250 
58.214 

0.01717 
0.01718 

246.16 

247.59 

14339 
14411 

1.961 
1.990 

114.2 
115.8 

137.2 

279.0 

1.07234 

58.179 

0.01719 

249.02 

14482 

2.018 

117.4 

137.9 
138.6 

T39J5T 
140.0 

280.3 
281.6 

1.07297 
1.07359 

58.145 
58.112 

0.01720 
0.01721 

250.34 
251.67 

14551 
14620 

2.045 
2.075 

118.9 
120.3 

282.8 
284.1 

1.07421 
1.07483 

58.078 
58.045 

0.01722 
0.01723 

252.90 
254.22 

14688 
14755 

2.098 
2.126 

121.7 
123.2 

140.8 

285.4 

1.07534 

58.012 

0.01724 

255.66     14821 

2.150 

124.7 

141.4 
142.0 

286.6 
287.8 

1.07594 
1.07653 

57.980 
57.948 

0.01725 
0.01726 

256.77 
258.00 

14886 
14951 

2.175 
2.202 

126.2 

127.7 

PROPERTIES  OF  STEAM. 


153 


TABLE  XXXIX. 

Steam. 

Total 
Ibs. 
persq. 
inch. 

pressure. 
Inches 
raercur. 

Tem- 
perat're 
Fahr. 

Volume 
water  = 
1  at  40. 

weight 
Ibs.  per 
cubic  ft. 

Bulk 
cubic  ft. 
per  Ib. 

Units 
Tola 
pound. 

of  heat 
Iper 
cubic  ft. 

rom  32° 
Latei 
pound. 

toT. 
t  per 
cubic  ft. 

lit 

P 

/ 

T 

if 

V 

G 

H 

H' 

L 

L' 

p 

14.7 
15 

29.92 
30.55 

212 
213 

1740 
1706 

0.0358 
0.0365 

27.897 
27.347 

1146.6 
1147.0 

41.100 
41.920 

965.7 
965.1 

34.61 
35.29 

.00 
.3 

16 

32.59 

216.4 

1601 

0.0389 

25.674 

1148.0 

44.700 

962.7 

37.50 

1 

17 
18 
19 

34.63 
36.67 
38.71 

219.6 
222.8 
225.7 

1509 
1426 
1353 

0.0413 
0.0437 
0.0461 

24.186 
22.865 
21.693 

1149.0!47.478 
1149.950.255 
1150.8  53.030 

960.4 
958.1 
956.0 

39.68 
41.86 
44.05 

2 
3 
4 

5 
6 

20 
21 

40.74 

42.78 

228.5 
231.2 

1288 
1228 

0.0484 
0.0508 

20.690 
19.678 

1151.7 
1152.6 

55.802 
58.572 

954.1 
952.2 

46.23 

48.41 

22 

44.82 

233.8 

1173 

0.0532 

18.804 

1153.4 

61.340 

950.7 

50.48 

7 

23 

24 

46.85 
48.89 

236.3 
238.7 

1123 
1078 

0.0555 
0.0579 

18.005 
17.272 

1154.2 
1155.0 

64.106 
66.870 

948.7 
946.0 

52.65 
54.82 

8 
9 

25 

26 

50.93 
52.97 

241.0 
243.3 

1035 
995.1 

0.0602 
0.0625 

16.597 
15.994 

1155.7 
1156.4 

69.632 
72.392 

945.4 
943.8 

56.96 
59.09 

10 
11 

27 

55.00 

245.4 

958.2 

0.0648 

15.422 

1157.1 

75.159 

942.3 

61.21 

12 

28 
29 

30 
31 

57.04 
59.08 

247.5 
249.4 

926.4 
895.6 

0.0672 
0.0696 

14.881 
14.371 

1157.7 
1158.2 

77.914 
70.667 

940.9 
939.6 

63.31 
65.41 

13 
14 

61.11 
63.15 

251.4 
253.4 

866.7 
838.3 

0.0720 
0.0743 

13.892 
13.456 

1158.7 
1159.3 

83.410 
86.162 

937.8 
936.4 

67.51 
69.60 

15    ! 
16 

32 

65.19 

255.3 

812.0 

0.076613.059 

1159.9  88.913 

935.1 

71.68 

17 

33 
34 

67.23 
69.26 

257.2 
259.0 

787.8 
765.7 

0.0789  12.669 
0.0812  12.313 

1160.5 
1161.0 

91.662 
94.411 

933.7 
932.4 

73.75 
75.83 

18 
19 

35 
36 
37 

71.30 
73.34 
75.38 

260.7 
262.4 
264.1 

745.8 
726.9 
708.8 

0.0834  11.955 
0.0860  11.624 
0.0884  11.309 

1161.5 
1162.0 
1162.5 

97.156 
99.901 
102.65 

931.2 
929.9 

928.7 

77.89 
79.95 
82.01 

20 
21 
22 

38 
39 

40~ 
41 

77.41 
79.45 

265.7 
267.3 

691.7 
675.4 

0.0908 
0.0930 

11.013 
10.745 

1163.0 
1163.5 

105.40 
108.15 

927.6 
926.4 

84.06 
86.10 

23 

24 

81.49 
83.52 

268.9 
270.4 

654.9 
640.0 

0.0952 
0.0974 

10.498 
10.262 

1164.0 
1164.5 

110.87 
113.61 

925.3 
924.3 

88.14 
90.18 

25 
26 

42 

85.56 

271.9 

625.4 

0.0997 

10.031 

1164.9 

116.35 

923.1 

92.21 

27 

43 
44 

45 

46 
47 

87.60 
89.64 

273.3 
274.8 

611.2 
597.4 

0.1020 
0.1044 

9.8030 
9.5801 

1165.4 
1165.8 

119.09 
121.83 

922.1 
921.1 

94.24 
96.26 

28 
29 

91.67 
93.71 
95.75 

276.2 
277.6 
279.0 

584.1 
571.9 
560.1 

0.1068 
0.1093 
0.1117 

9.3617 
9.1465 
8.9486 

1166.2 
1166.7 
1167.2 

124.57 
127.31 
130.05 

920.1 
919.1 
918.0 

98.28 
100.3 
102.3 

30 
31 
32 

48 
49 

97.78 
99.82 

280.3 
281.6 

548.8 
537.8 

0.1141 
0.1166 

8.7596 
8.5776 

1167.6 
1168.0 

132.79 
135.53 

917.1 
916.2 

104.3 
106.3 

33 
34 

50 
51 

101.86 
103.90 

282.8 
284.1 

527.2 
517.5 

0.1183 
0.1206 

8.4504 
8.2899 

1168.4 
1168.8 

138.27 
141.00 

915.4 
914.5 

108.3 
110.3 

35 
36 

52 

105.93 

285.4 

507.1 

0.1230 

8.1284 

1169.2 

143.73 

913.6 

112.3 

37 

53 

54 

107.97 
110.01 

286.6 
287.8 

498.0 
489.2 

0.1254 
0.1278 

7.9724 
7.8249 

1169.5  146.46 
1169.8  149.18 

912.7 
911.8 

114.3 
116.3 

38 
39 

154 


PROPERTIES  OF   WATER. 


TABLE  XL. 

"Water. 

Temperature 

Volume. 

Weight. 
Ibs.  per 
cubic  ft. 

Bulk, 
cubic  feet 
per  pound. 

Units  of  h 
Tola 
pound. 

eat  in  wate 
1  per 
cubic  foot. 

h'. 

15014 
15075 
15135 
15195 

1  5-J.-.4 

r  from  31 
Lateu 
pound. 

L 

2.230 
2.260 
2.286 
2.310 

•_'.:i:  ;.-> 

•°  to  T. 

tper 
cubic  ft. 

f. 

129.2 
130.8 
132.2 
133.5 
134.7 

Cent. 

Fahr. 

1  at  40°. 

~v~~ 

1.07720 
1.07778 
1.07835 
1.07892 
1.07943 

142.8 
143.4 
144.0 
144.6 
145.2 

T 

289.0 
290.2 
291.3 
292.4 
293.6 

? 
57.917 
57.886 
57.857 
57.823 
57.795 

e 

0.01726 
0.01727 
0.01728 
0.01729 
0.01730 

h. 

259.23 
260.46 
261.58 
262.71 
263.93 

145.9 
146.6 
147.1 
147.7 
148.3 

294.7 
295.8 
296.9 
298.0 
299.0 

1.07998 
1.08051 
1.08104 
1.08157 
1.08209 

f>7.7(>S 
57.739 
57.711 
57.683 
57.655 

0.01731 
0.01732 
0.01733 
0.01734 
0.01735 

265.05 
266.18 
267.30 
268.43 

269.45 

15312 
15368 
15424 
15480 
15535 

2.354 

2.382 
2.406 
2.430 
2.454 

136.0 
137.4 
138.8 
140.2 
141.6 

148.8 
149.3 
150.0 
150.5 
151.1 

300.0 
301.0 
302.0 
303.0 
304.0 

1.08259 
1.08311 
1.08362 
1.08411 
1.08460 

57.629 
57.604 
57.579 
57.546 
57.522 

0.01736 
0.01737 
0.01738 
0.01738 
0.01739 

270.48 
271.50 
272.52 
273.55 
274.58 

l.j-)SS 
15641 
15693 
15746 
15797 

2.480 
2.503 
2.525 
2.548 
2.572 

142.9 
144.2 
145.5 

146.7 

147.8 

151.6 
152.2 
152.8 
153.3 
153.8 

305.0 
306.0 
307.0 
307.9 
308.9 

1.08507 
1.08556 
1.08604 
1.08653 
1.08700 

57.497 
57.472 
57.447 
57.420 
57.395 

57.370 
57.346 
57.322 
57.298 
57.275 

0.01740 
0.01740 
0.01741 
0.01741 
0.01742 

"001743" 
0.01743 
0.01744 
0.01745 
0.01745 

275.60 
276.62 
277.64 
278.56 
279.58 

15846 
15896 
15945 
15995 
16044 

2.51)0 
2.618 
2.640 
2.658 
2.686 

149.2 
150.4 
151.6 
152.8 
154.1 

154.3 
154.8 
155.1 
155.9 
156.3 

309.8 
310.7 
311.6 
312.5 
313.4 

1.08747 

1.08792 
1.08838 
1.08883 
1.08928 

280.51 
281.43 
282.35 
283.27 
284.19 

16093 
16140 
16187 
16233 
16278 

2.707 
2.728 
2.755 
2.776 
2.795 

155.3 
156.6 
157.9 
159.2 
160.4 

156.8 
157.3 

157.7 
158.1 
158.6 

314.3 
315.1 
315.9 
316.7 
317.5 

1.08971 
1.09014 
1.09057 
1.09100 
1.09138 

T09180~ 
1.09222 
1.09264 
1.09305 
1.09346 

.->7.L>.-,i> 
57.230 
57.208 
57.186 
57.164 

0.01746 
0.01747 
0.01747 
0.01748 
0.01749 

285.12 
285.94 
286.76 
287.58 
288.40 

289.32 
290.14 
290.96 
291.78 
292.60 

16324 
16368 
16411 
16453 
16493 

2.K22 
2.840 
2.860 
2.881 
2.900 

161.6 
162.7 
165.8 
164.8 
105.9 

159.1 
159.6 
160.0 
160.4 
160.8 

318.4 
319.2 
320.0 
320.8 
321.6 

57.142 
57.121 
57.100 
57.078 
57.057 

0.01750 
0.01750 
0.01751 
0.01752 
0.01752 

16533 
16574 
16614 
16654 
16695 

2.920 
2.940 
2.960 
2.980 
3.000 

166.9 

168.0 
169.1 
170.2 
171.3 

161.2 
161.6 
162.2 
162.6 
163.0 

322.4 
323.2 
324.0 
324.7 
325.4 

1.09384 
1.09425 
1.09465 
1.09506 
1.09546 

57.036 
57.015 
56.994 
56.973 
56.953 

0.01753 
0.01754 
0.01754 
0.01755 
0.01755 

293.42 
294.25 
295.07 
295.79 
296.5 

16735 
16774 
1C813 
16852 
16890 

3.022 
3.047 
3.068 
3.089 
3.100 

172.4 
173.5 
174.6 

175.7 
176.7 

PROPERTIES   OF  STEAM. 


155 


TABLE   XLI. 

Steam. 

Total  i 
Ibs. 

mrsij. 
inch. 

P 

>ressure. 
Inches 
uiercur. 

Tem- 
jerat're 
Fahr. 

Volume 
water  = 
1  at  40. 

weight 
Ibs.  per 
cubic  ft. 

Bulk 
cubic  ft. 
per  Ib. 

Unite 

Tata 
pound. 

of  heat  f 
per 
cubic  ft. 

rom32° 
Laten 
pound. 

toT. 
tper 
cubic  ft. 

111 

H! 

/ 

T 

t 

$ 

G 

H 

H' 

L 

L' 

p 

55 

56 

112.04 
114.08 

289.0 
290.2 

480.6 
472.1 

0.1298 
0.1302 

7.7028 
7.6774 

1170.1 
1170.5 

151.91 
154.64 

910.9 
910.1 

118.3 
120.3 

40 

41 

57 

116.12 

291.3 

464.0 

0.1324 

7.5524 

1170.9 

157.37 

909.9 

122.2 

42 

58 
59 

118.16 
120.19 

292.4 
293.6 

456.2 
448.8 

0.1346 
0.1388 

7.4277 
7.2034 

1171.3 
1171.6 

160.10 
162.83 

908.6 
907.7 

124.2 
126.1 

43 
44 

60 
61 

122.23 
124.27 

294.7 
295.8 

441.6 
434.6 

0.1422 
0.1434 

7.0786 
6.9709 

1171.9 
1172.3 

165.56 
168.28 

906.9 
906.1 

128.1 
130.0 

45 
46 

62 

126.30 

296.9 

427.8 

0.1456 

6.8643 

1172.6 

171.00 

905.3 

131.9 

47 

63 
64 

66 

128.34 
130.38 

298.0 
299.0 

421.2 
414.9 

0.1479 
0.1502 

6.7588 
6.6543 

1172.9 
1  143.2 

173.71 
176.41 

904.5 
903.8 

133.9 
135.8 

48 
49 

132.42 
134.45 

300.0 
301.0 

4  OS.  -7 
402.6 

0.1526 
0.1548 

6.5510 
6.4570 

1173.5 

1173.8 

179.13 
181.84 

903.0 
902.3 

137.8 
139.7 

50 
51 

67 

136.49 

302.0 

396.7 

0.1571 

6.3660 

1174.1 

184.53 

901.6 

141.7 

52 

63 
69 

138.53 
140.36 

303.0 
304.0 

391.1 
385.6 

0.1593 
0.1616 

6.2750 
6.1852 

1174.4 
1174.7 

187.24 
190.00 

900.9 
900.1 

143.6 
145.6 

53 
54 

70 
71 

142.60 
144.64 

305.0 
306.0 

380.4 
374.7 

0.1640 
0.1662 

6.0972 
6.0162 

1175.0 
1175.3 

192.71 
195.42 

899.4 
898.7 

147.5 
149.5 

55 
56 

72 

146.68 

307.0 

369.5 

0.1684  5.9363 

1175.6 

198.14 

898.0 

151.4 

57 

73 
74 

148.72 
150.75 

307.9 
308.9 

364.7 
360.2 

0.1707 
0.1730 

5.8576 
5.7799 

1175.9 
1176.2 

200.85 
203.58 

897.4 
896.6 

153.3 
155.2 

58 
59 

75 
76 

152.79 
154.83 

309.8 
310.7 

355.8 
351.1 

0.1753 
0.1775 

5.7033 
5.6324 

1176.5 

1176.8 

206.29 
209.00 

896.0 
895.4 

157.1 
159.0 

60 
61 

77 

156.86 

311.6 

346.6 

0.1798 

5.5624 

1177.1 

211.71 

895.8 

160.9 

62 

78 
79 

158.90 
160.94 

312.5 
313.4 

342.3 
338.1 

0.1820 
0.1843 

5.4933 
5.4251 

1177.4 
1177.6 

214.42 
217.13 

894.1 
893.4 

162.8 
164.7 

63 

64 

80 
81 

162.98 
165.01 

314.3 
315.1 

334.3 
330.3 

0.1866 
0.1888 

5.3576 
5.2947 

1177.8 
1178.1 

219.84 
222.55 

892.7 
892.2 

166.6 
168.5 

65 
66 

82 

167.05 

315.9 

326.4 

0.1911 

5.2327 

1178.4 

225.25 

891.7 

170.4 

67 

83 
84 

169.09 
171.12 

316.7 
317.5 

322.6 

318.8 

0.1926 
0.1956 

5.1916 
5.1114 

1178.7 
1178.9 

227.96 
230.68 

891.1 
890.5 

172.3 
174.2 

68 
69 

70 
71 

85 
86 

173.16 
175.20 

318.4 
319.2 

315.2 
311.7 

0.1979 
0.2002 

5.0522 
4.9955 

1179.1 
1179.4 

233.38 
236.09 

889.8 
889.3 

176.1 
178.0 

87 

177.24 

320.0 

308.2 

0.2024 

4.9399 

1179.7 

238.79 

888.8 

179.9 

72 

88 
89 

179.27 
181.31 

320.8 
321.6 

304.8 
301.5 

0.2047 
0.2069 

4.8855 
4.8322 

1179.9 
1180.1 

241.50 
244.21 

888.1 
887.5- 

181.8 
183.6 

73 

74 

90    183.35 
91     185.38 

322.4 
323.2 

298.2 
295.0 

0.2092 
0.2114 

4.7803 
4.7293 

1180.3 
1180.6 

246.91 
249.62 

886.9 
886.4 

185.4 
187.3 

75 

76 

92    187.32 

324.0 

291.9 

0.2137 

4.6794 

1180.9 

252.33 

885.9 

189.2 

77 

93    189.46 
94    191.50 

324.7 
325.4 

288.9 
285.9 

0.2159 
0.2182 

4.6305 

4.5827 

1181.1 
1181.3 

255.04 
257.75 

885.3 
884.8 

191.0 
193.2 

78 
79 

156 


PROPERTIES   OF   WATER. 


TABLE  XLII. 

Water. 

Temperature 

of  the  water. 

Volume, 
water  = 

Weight. 
Ibs.  per 

Bulk, 
cubic  feet 

Units  of  heat  in  wate 
Total  per 

r  from  32°  to  T. 
Latent  per 

Cent. 

.Fahr. 

1  at  40°. 

cubic  ft. 

per  pound. 

pound. 

cubic  foot. 

pound. 

cubic  ft. 

T 

T 

V 

? 

e 

h. 

h'. 

I. 

I'. 

163.4 

326.2 

1.09578 

56.934 

0.01756 

297.32 

16928 

3.121 

177.7 

163.8 

327.0 

1.09617 

56.914 

0.01756 

298.14 

16966 

3.142 

178.8 

164.2 

327.7 

1.09655 

56.894 

0.01757 

298.86 

17004 

3.163 

179.9 

164.6 

328.5 

1.09092 

56.875 

0.01758 

299.68 

17046 

3.183 

181.0 

165.0 

329.2 

1.09730 

56.855 

0.01758 

300.40 

17078 

S.204 

182.1 

165.4 

329.9 

1.09768 

56.836 

0.017.7.) 

301.12 

17114 

3.222 

ls:;.i 

165.9 

330.7 

1.09804 

56.818 

0.01759 

301.94 

17149 

3.240 

184.1 

166.3 

331.3 

1.09840 

56.804 

0.01760 

302.56 

17183 

3.258 

185.1 

166.7 

331.9 

1.09876 

56.786 

0.01760 

303.17 

17217 

3.276 

186.0 

167.0 

332.6 

1.09911 

5(5.7(59 

0.01761 

;;o:j,st) 

17251 

3.294 

186.9 

167.3 

333.3 

1.09949 

5(5.743 

0.01761 

:;o  1.111 

17284 

3.312 

187.9 

167.7 

334.0 

1.09984 

56.725 

0.01762 

305.33 

17318 

3.330 

189.0 

168.0 

334.7 

1.10019 

56.706 

0.01763 

306.05 

17350 

3.349 

190.0 

168.4 

335.4 

1.10055 

56.688 

0.01763 

306.77 

17384 

3.368 

191.0 

168.8 

336.1 

1.10091 

56.670 

0.01764 

307.49 

17427 

3.387 

192.0 

169.2 

336.8 

1.10125 

56.652 

0.01764 

308.21 

17461 

3.406 

193.0 

169.6 

337.4 

1.10159 

56.635 

0.01765 

308.82 

17493 

3.425 

194.0 

170.0 

338.0 

1.10193 

56.618 

0.01766 

309.44 

17525 

3.444 

195.0 

170.4 

338.7 

1.10226 

56.600 

0.01766 

310.16 

17557 

3.462 

196.0 

170.8 

339.4 

1.10260 

56.583 

0.01767 

310.88 

17589 

3.481 

197.0 

171.1 

340.0 

1.10292 

56.566 

0.01768 

311.50 

17(521 

3.500 

198.0 

172.9 

343.2 

1.10459 

56.483 

0.01770 

314.79 

17772 

3.590 

202.8 

174.5 

346.2 

1.10627 

56.403 

0.01773 

317.88 

17921 

3.678 

207.5 

176.2 

349.2 

1.10787 

56.326 

0.01775 

320.96 

18068 

3.763 

212.1 

177.7 

352.0 

1.10940 

56.236 

0.01778 

:;-j:;.s.-) 

18212 

3.850 

216.5 

179.2 

354.8 

1.11070 

56.166 

0.01780 

326.73 

18349 

3.927 

220.8 

180.7 

357.4 

1.11208 

56.098 

0.01782 

329.41 

18481 

4.010 

225.0 

182/2 

360.0 

1.11344 

56.031 

0.01784 

332.09 

18607 

4.090 

229.0 

183.7 

362.5 

1.11478 

55.965 

0.01787 

334.67 

18730 

4.168 

233.3 

185.0 

365.0 

1.11613 

55.900 

0.01789 

337.24 

18850 

4.244 

237.2 

186.5 

367.4 

1.11742 

55.834 

0.01791 

339.72 

18966 

4.318 

241.0 

188.0 

369.8 

1.11869 

55.770 

0.01793 

342.19 

19080 

4.390 

244.6 

188.5 

372:0 

1.11993 

55.708 

0.01795 

344.46 

19190 

4.460 

248.5 

190.0 

374.2 

112109 

55.648 

0.01797 

346.73 

19296 

4.530 

252.1 

191.2 

376.4 

1.12227 

55.591 

0.01799 

349.00 

19399 

4.598 

255.7 

192.5 

378.5 

112343 

55.534 

0.01800 

351.16 

19501 

4.666 

259.1 

193.7 

380.6 

1.12456 

55.477 

0.01802 

353.33 

19602 

4.731 

262.5 

194.4 

382.6 

1.12561 

55.426 

0.01804 

355.39 

19698 

4.794 

265.7 

197.0 

386.6 

1.12783 

55.317 

0.01807 

359.54 

19885 

4.940 

272.8 

199.1 

390.4 

1.13000 

55.211 

0.01811 

363.48 

20068 

5.0S2 

279.8 

PROPERTIES  OF  STEAM. 


157 


TABLE  XLIII. 
Steam. 

Total  i 
Ibs. 
aersq. 
inch. 

>ressure. 
Inches 

inercur. 

Tem- 
perat're 
Fahr. 

Volume 
water  = 
1  at  40. 

Weight 
Ibs.  per 
cubic  ft. 

Bulk 
cubic  ft. 
per  Ib. 

Units  of  heat 
Total  per 
pound,   cubic  ft. 

Jom32° 
pound. 

to  f, 

t  per 

cubic  ft. 

1'rcssiire 
above  at- 
mosphere. 

P 

96 
97 
98 
99 

193.53 
195.57 
197.61 
199.65 
201.68 

T 

326.2 
327.0 
327.7 
328.5 
329.2 

283.0 
280.2 
277.4 
274.7 
272.0 

f 

0.2204 
0.2227 
0.2249 
0.2271 
0.2294 

G 

4.5361 
4.4902 
4.4454 
4.4017 
4.3591 

H 

1181.5 
1181.8 
1182.1 
1182.3 
1182.5 

H' 

260.46 
263.16 
265.86 
268.55 

271.2:; 

L 

884.2 
883.8 
883.3 
882.6 
882.1 

L' 

194.9 
196.7 
198.6 
200.4 
202.3 

P 

80 
81 
82 
83 

84 

100 

101 
102 
103 
104 

107 
108 
109 

203.72 
205.76 
207.79 
209.83 
211.87 

329.9 
330.7 
331.3 
331.9 
332.6 

269.4 
266.8 
264.3 
261.8 
259.4 

0.2316 
0.2338 
0.2360 
0.2382 
0.2405 

4.:;  17ti 
4.2769 
4.2367 
4.1970 
4.1577 

1182.7 
1182.9 
1183.1 
1183.3 
1183.5 

273.93 

276.63 
279.32 
282.62 
284.70 

881.6 
881.0 
880.6 
880.1 
879.6 

204.2 
206.1 
208.0 
209.8 
211.6 

85 
86 
87 
88 
89 

213.91 
215.94 
217.98 
220.02 
222.06 

333.3    257.0 
334.0    254.6 
334.7  j  252.3 
335.4    250.1 
336.1    247.9 

0.242814.1187 
0.24504.0813 
0.2472  4.0444 
o.2  ]'.'•'>  4.0081 
0.2517  3.9723 

1183.7 
1183.9 
1184.1 
1184.3 
1184.5 

287.40 
290.09 
292.78 
295.48 
298.18 

879.1 
879.6 
878.1 
877.5 
877.0 

213.4 
215.2 
217.0 
218.9 
220.7 

90 
91 
92 
93 
94 

110 
111 
112 
113 
114 

TuT 

120 
125 
130 
135 

MO" 

145 
150 
155 
160 

"l65~ 
170 
175 
180 
185 

224.10 
226.13 
228.17 
230.20 
232.24 

336.8 
337.4 
338.0 
338.7 
339.4 

245.7 
243.5 
241.4 
239.3 
237.3 

0.2540  3.9376 
0.256H3.9036 
0.258413.8701 
0.2603|  3.8411 
0.26283.8047 

1184.7 
1184.9 
1185.1 
1185.3 
1185.5 

300.87 
303.56 
306.26 
308.94 
311.65 

876.5 
876.1 
875.7 
875.1 
874.6 

222.6 
224.4 
226.3 
228.1 
229.9 

95 
96 
97 
98 
99 

234.28 
244.4 
254.6 
264.8 
275.0 

340.0 
343.2 
346.2 
349.2 
352.0 

235.3 
226.0 
217.2 
209.1 
201.4 

0.265113.7722 
0.2759  1  3.6244 
0.2867  3.4875 
0.2984'  3.3516 
0.3098  j  3.2278 

1185.7 
1186.6 
1187.5 
1188.4 
1189.3 

314.33 

327.89 
341.44 
355.00 
368.55 

874.2 
873.8 
869.6 
867.4 
865.5 

231.8 
241.0 
250.1 
259.0 
268.1 

100 
105 
110 
115 
120 

285.2 
295.4 
305.6 
310.8 
325.9 

354.8 
357.4 
360.0 
362.5 
365.0 

194.3 
187.8 
181.8 
176.5 
171.5 

0.3212,3.1139 
0.3322;  3.0105 
0.34321  2.9136 
0.3534!  2.8289 
0.36462.7432 

1190.1 
1190.9 
1191.7 
1192.5 
1193.3 

381.88 
395.16 
408.38 
421.54 
435.08 

863.5 
861.5 
859.6 
857.8 
856.1 

277.0 
275.8 
294.5 
303.2 
312.1 

125 
130 
135 
140 
145 

336.0 
346.3 
356.5 
366.7 
376.9 

367.4 
369.8 
372.0 
374.2 
376.4 

166.6 
161.1 
157.0 
152.8 
148.8 

0.37562.6617 
0.38712.5831 
0.39732.5171 
0.4075  2.4541 
0.4182;2.3916 

1194.0 
1194.7 
1195.4 
1196.1 
1196.8 

448.64 
462.22 
475.80 
488.96 
502.10 

854.3 
852.5 
851.0 
849.4 
847.8 

321.0 
329.9 
338.7 
347.1 
355.5 

150 
155 
160 
165 
170 

190    378.1 
195    387.3 
200    407.4 
210    427.8 
220  '448.2 

378.5 
380.6 
382.6 
386.6 
390.4 

145.0 
141.5 
138.1 
132.0 
126.3 

0.4292:  2.3299 
0.4409,2.2684 
0.4517  2.2137 
0.4719'  2.1  192 
0.4935  12.0265 

1197.4 
1198.1 
1198.7 
1199.8 
1201.0 

515.20 
528.27 
542.07 
568.40 
574.70 

846.2 
844.8 
843.3 
840.3 
837.5 

363.9 
372.4 
381.0 
398.0 
414.8 

175 
180 
185 
195 
205 

158 


PROPERTIES   OF   WATER. 


TABLE  XLIV. 
"Water. 

Tt-mpe 
of  the 
Cent. 

rature 
water. 
Fahr. 

Volume, 
water  = 
1  at  40°. 

~V~~ 
1.13210 
1.13301 
1.13577 
1.13760 
1.13944 

Weight. 
Ibs.  per 
cubic  ft. 

Bulk. 

cubic  feet 
per  pound. 

Unite  of 
Tots 
pound. 

icat  in  wat 
1  per 
cubic  foot. 

er  from  C 
I.iit'-i 
pound. 

i  .„'/. 

tper 
cubic  ft. 

~l'~ 

286.6 
292.9 
299.1 
305.2 
311.2 

T 

201.1 
203.5 
205.0 

206.8 
208.7 

T 

394.0 
397.6 
401.0 
404.3 
407.5 

f 

55.108 
55.017 
54.926 
54.838 
54.752 

e 

0.01814 
0.01817 
0.01821 
0.01824 
0.01826 

h. 

367.20 
370.92 
374.44 
357.86 
381.18 

h'. 

20236 
20402 
20561 
20720 

L'OSTO 

I. 

5.200 
5.318 
5.437 
5.558 
5.679 

210.2 
211.9 
213.6 
215.1 
216.7 

410.6 
413.5 
416.5 
419.2 
422.1 

1.14119 
1.14285 
1.14441 

1.14589 
1.14743 

54.670 
54.590 
54.514 
54.440 
54.367 

0.01829 
0.01832 
0.01834 
0.01837 
0.01839 

liSJ.II) 
387.40 
390.50 
393.31 

3!)0.:;i 

21015 
21147 
21273 
21394 
21510 

5.800 
5.903 
6.006 
6.109 
6.212 

317.1 
324.6 
332.0 
339.5 
346.7 

~353T 
356.9 
359.9 
362.8 
365.6 

218.2 
219.6 
221.1 
222.4 
223.6 

424.8 
427.4 
430.0 
432.4 
434.9 

~43L3~ 
439.6 
441.9 
444.1 
446.4 

1.14897 
1.15050 
1.15202 
1.15339 
1.15481 

54.299 
54.230 
54.161 
54.093 
54.024 

0.01841 
0.01844 
0.01846 
0.01849 
0.01851 

399.11 

401.82 
404.52 
407.02 
409.63 

21622 
21751 
21876 
21997 
22114 

6.315 
6.418 
6.521 
6.624 
6.727 

225.1 

226.4 
227.7 
228.9 
230.2 

281.4 

232.5 
233.6 
234.7 
235.9 

1.15621 
1.15764 
1.15880 
1.16003 
1.16127 

53.959 
53.895 
53.834 
53.777 
53.721 

0.01853 
0.01856 
0.01858 
0.01859 
0.01861 

412.13 
414.53 
416.92 
419.21 
421.60 

22238 
22347 
22452 
22553 
22650 

6.830 
6.926 
7.020 
7.111 
7.200 

368.5 
373.2 
377.9 
382.5 
386.9 

391.1 
395.3 
399.4 
403.6 
407.3 

448.5 
450.6 
452.6 
454.6 
456.7 

1.16250 
1.16372 
1.16494 
1.16571 
1.16695 

53.667 
53.614 
53.563 
53.513 
53.455 

0.01863 
0.01865 
0.01867 
0.01869 
0.01871 

423.79 
425.97 
428.06 
430.14 
432.32 

22744 
22843 
22938 
23029 
23116 

7.288 
7.374 
7.459 
7.542 
7.623 

237.0 
238.0 
239.0 
241.1 
244.1 

~24675~ 
248.8 
253.1 
257.2 
261.0 

458.7 
460.6 
462.5 
466.1 
471.5 

1.16818 
1.16942 
1.17066 
1.17274 
1.17598 

53.406 
53.352 
53.293 
53.158 
53.027 

0.01872 
0.01874 
0.01876 
0.01881 
0.01886 

434.40 
436.38 
438.39 
442.21 
447.83 

23200 
23282 
23363 
23555 
23741 

7.700 
7.787 
7.893 
8.113 
8.329 

411.2 
415.5 
423.3 
433.2 
442.9 

475.7 
479.8 
487.6 
494.9 
501.8 

1.17917 
1.18231 
1.18531 
1.18961 
1.19343 

52.900 
52.768 
52.588 
52.430 
52.264 

52.102 
51.943 
51.787 
51.642 
51.498 

0.01890 
0.01895 
0.01901 
0.01907 
0.01913 

~aoi9~i{f 

0.01925 
0.01931 
0.01936 
0.01942 

452.24 
456.55 
464.66 
472.28 
479.51 

23923 
24091 
24436 
24762 
25061 

8.541 
8.747 
9.060 
9.381 
9.710 

452.4 
461.6 
476.5 
491.8 
507.5 

263.5 
268.1 
271.9 
273.3 
277.5 

508.4 
514.6 
521.4 
526.0 
531.6 

1.19742 
1.20131 
1.20562 
1.20812 
1.21147 

486.40 
492.97 
500.14 
505.00 

510.S4 

25577 
25606 
25901 
26079 
26307 

10.00 
10.37 
10.74 
11.00 
11.242 

521.0 

538.7 
556.2 
568.1 
578.8 

PROPERTIES  OF  STEAM. 


159 


TABLE  XLV. 
Steam. 

Total 
Ibs. 
per  so., 
inch. 

>ressure. 
Inches 
inercur. 

Tem- 

pi-riit're 

Fahr. 

Volume 
water  = 
1  at  40. 

Weight 

Hi-.  |MT 

cubic  fl. 

Bulk 
cubic  ft. 
per  Ib. 

Units  of  heat 
Total  per 
pound,  cubic  ft. 

rom  32° 
Later 
pound. 

toT. 

t  per 
cubic  ft. 

m 

n 

P 

230 
240 
250 
260 
270 

/ 

468.5 
488.9 
509.3 
529.7 
550.0 

T 

394.0 
397.6 
401.0 
404.3 
407.5 

If 
120.8 
116.1 
111.7 
107.5 
103.7 

«A 

tP 
0.5165 
0.5364 
0.5595 
0.4803 
0.6016 

G 

1.9360 
1.8646 
1.7874 
1.7230 
1.6621 

H 

1202.2 
1203.2 
1204.2 
1205.2 
1206.2 

H' 

620.96 
(J47.41 
673.85 
700.28 
726.66 

L 

835.0 
832.3 
829.8 

827.4 
825.0 

11 

431.3 
447.9 
464.4 

480.8 
497.1 

P 

215 
225 
235 
245 
255 

280 
290 
300 
310 
320 

570.4 
590.8 
611.1 
631.5 
651.9 

410.6 
413.5 
416.5 
419.2 
422.1 

100.2 
97.01 
94.22 
91.13 
88.21 

0.6238 
0.6459 
0.6681 
0.6896 

0.7107 

1.6031 
1.5481 
1.4967 
1.4499 
1.4071 

l~207".2 
1208.1 
1209.0 
1209.8 
1210.6 

753.04 
779.40 
805.74 
832.96 
858.36 

822.8 

820.7 
818.6 
816.5 
814.4 

513.3 
529.4 
545.4 
561.4 
577.3 

265 
275 
285 
295 
305 

330 
340 
350 
360 
370 

672.3 
692.6 
713.0 
733.4 
753.8 

424.8 
427.4 
430.0 
432.4 
434.9 

85.44 
83.19 
80.99 
78.84 
76.74 

0.7302  1.3695 
0.7547  1.3250 
0.7745  1.2915 
0.7943  1.259U 
0.81461.2275 

1211.5 
1212.3 
1213.1 
1213.9 
1214.7 

884.63 
910.89 
937.13 
963.34 
989.51 

812.4 
810.5 
808.6 
806.9 
805.1 

593.2 
608.9 
624.5 
640.2 
655.8 

315 
325 
335 

345 
355 

380 
390 
400 
410 
420 

774.1 
794.5 
814.9 
835.2 
855.6 

437.3 
439.6 
441.9 
444.1 
446.4 

74.66 
72.90 
71.19 
69.52 
67.90 

0.8353 
0.8626 
0.8745 
0.8952 
0.9142 

1.1968 
1.1597 
1.1434 
1.1170 
1.0938 

1215.5 
1216.2 
1217.9 
1218.6 
1219.3 

1015.7 
1041.8 
1067.9 
1094.0 
1120.2 

803.4 
801.7 
800.0 
799.4 
797.7 

671.3 
686.7 
702.0 
717.2 
732.4 

365 
375 
385 
395 
405 

430 
440 
450 
460 
470 

876.0 
896.4 
916.7 
937.1 
957.5 

448.5 
450.6 
452.6 
454.6 
456.7 

66.34 
64.91 
63.55 
62.22 
60.94 

0.9400  1.0634 
0.9599  1.0417 
0.9804  i  1.0201 
1.00070.9993 
1.0211  jO.9793 

1218.8 
1219.5 
1220.1 
1220.7 
1221.3 

1146.3 
1172.3 
1198.3 
1124.3 
1150.4 

795.0 
793.5 
792.0 
790.5 
789.0 

747.6 
762.8 
777.9 
792.9 
807.8 

415 
425 
435 
445 
455 

4SO 
490 

500 
525 
550 

1X5 
600 
650 
700 
750 

977.8 
998.2 
1018.6 
1069.5 
1120.4 

458.7 
460.6 
462.5 
466.1 
471.5 

59.72 
58.54 
57.45 
54.81 
52.47 

1.  0446^0.9573 

1.0t552  0.9388 
1.0859  0.9209 
1.1381:0.8786 
1.1890  0.8410 

1221.9 
1222.5 
1223.0 
1224.5 
1225.8 

1276.5 
1302.3 
1328.1 
1392.6 
1456.9 

787.5 
786.1 
784.7 
782.3 
778.0 

822.7 
837.4 
852.1 
881.8 
921.3 

465 
475 
485 
510 
535 

1171.4 
1222.3 
1324.2 
1426.0 
1527.9 

475.7 
479.8 
487.6 
494.9 
501.8 

50.32 
48.35 
44.75 

41.70 
39.05 

1.2397 
1.2901 
1.3943 
1.4961 
1.5977 

0.8066 
0.7751 
0.7172 
0.6684 
0.6259 

1227.2 
1228.3 
1230.6 
1232.7 
1234.9 

1521.0 

1584.8 
1709.5 
1933.8 
2057.7 

775.0 
771.8 
766.0 
760.4 
755.4 

960.4 
1000 
1082 
1157 
1234 

560 
585 
635 
685 
735 

800  1629.8 
850  1731.6 
900  1833.5 
'.)•><»  1935.5 
1000  2037.2 

508.4 
514.6 
521.4 
526.0 
531.6 

36.73 
34.68 
32.87 
31.21 
29.73 

1.6986  0.5887 
1.7989  0.5554 
1.8979  0.5269 
1.9992  0.5002 
2.098610.4766 

1237.0 
1238.9 
1241.0 
1242.4 
1243.5 

2101.2 
2228.3 
2355.4 
2482.5 
2609.6 

750.6 
745.9 
740.0 
737.4 
732.3 

1307 
1374 
1435 
1490 
1538 

785 
835 
885 
935 
985 

160 


MEAN  PRESSURE. 


TABLE    XLVI. 

Mean  Pressure  of  Expanding  Steam. 

Absolute 
steam 
pressure. 

P 

1.333 
1 

On 

1.5 
Stea 
t 

Ie  of  expansion  of 
1.6      |        2 
lu  cut  off  at  I,  from 
I               * 

team,  denoted  by  3 
2.666         3 
beginning  of  strok 
1               i 

t. 
4 
e. 
| 

8 
1 

0.5 
1 

0.4826 
0.9652 

0.4683 
0.9367 

0.4587 
0.9175 

0.4232 
0.8465 

0.3713 
0.7426 

0.3497 
0.6995 

O.-J'.IS-J 
0.5965 

0.1924 
0.3849 

2 

1.9304 

1.8734 

1.8350 

1.6931 

1.4482 

1.3991 

1.1931 

0.7698 

3 

4 

2.8956 
3.8608 

2.8100 
3.7468 

2.7524 
3.6700 

2.5396 
3.3862 

2.2280 
2.8964 

2.0986 
2.7982 

1.7897 
2.3862 

1.1548 
1.5396 

5 
6 

4.8262 
5.7914 

4.6835 
5.6202 

4.587;-, 
5.5050 

4.2328 
5.0794 

3.7133 
4.4559 

3.4977 
4.1972 

•J.'.ix-js 
3.5794 

1.9246 
2.3095 

7 

6.7566 

6.5569 

6.4225 

5.9260 

5.1966 

4.8967 

4.1760 

2.6944 

8 
9 

7.7216 
8.6866 

7.4936 
8.5303 

7.3400 
8.2574 

6.7726 
7.6192 

5.9413 
6.6840 

5.5963 
6.2958 

4.7726 
5.3692 

3.0794 
3.4643 

10 
11 

9.6524 
10.617 

9.3670 
10.304 

9.1750 
10.092 

8.4657 
9.3123 

7.4267 
8.1694 

6.9954 
7.6949 

5.9657 
6.5622 

:;»<>:; 
4.2342 

12 

11.583 

11.240 

11.010 

10.159 

8.9121 

8.3944 

7.1589 

4.6191 

13 
14 

12.548 
13.513 

12.177 
13.113 

14.050 

14.987 

11.927 
12.845 

11.005 
11.852 

12.69S~ 
13.545 

9.6548 
10.397 

9.0940 
9.7935 

7.7555 
8.3520 

5.0041 
5.3890 

15 

16 

14.478 
15.443 

13.762 
14.679 

11.140 

11.882 

10.493 
11.192 

8.94So 
9.5451 

5.7739 

6.1588 

17 

16.408 

15.923 

15.597 

14.392 

12.625 

11.892 

10.141 

6.5437 

18 
19 

17.373 
18.339 

16.860 
17.797 

16.514 
17.432 

15.238 
16.085 

13.368 
14.110 

12.591 
13.291 

10.738 
11.335 

6.9287 
7.3136 

20 
21 

19.304 

20.269 

18.734 
19.671 

18.350 
19.268 

16.931 

17.778 

14.853 
15.596 

13.991 
14.690 

11.931 

12.527 

7.6986 
8.0835 

22 

21.234 

20.508 

20.185 

18.625 

16.339 

15.390 

13.124 

8.4684 

23 

24 

22.199 
23.165 

21.545 
22.481 

21.103 
22.020 

19.471 
20.318 

17.082 
17.823 

16.089 
16.789 

13.720 
14.317 

8.8534 
9.2383 

25 

26 

24.130 
25.096 

23.481 
24.355 

•J2.1C5S 
23.855 

21.164 
22.011 

18.567 
19.318 

17.488 
18.188 

14.913 
15.511 

9.6232 
10.008 

27 

26.061 

25.291 

24.773 

22.857 

20.052 

18.887 

16.107 

10.393 

28 
29 

27.026 
27.991 

28.956 
29.920 

26.228 
27.165 

25.690 
26.607 

23.704 
24.551 

20.795 
21.538 

19.587 
20.287 

16.704 
17.300 

10.778 
11.162 

30 
31 

28.100 
29.036 

27.524 
28.440 

25.396 
26.244 

22.280 
23.022 

20.986 
21.684 

17.897 
18.493 

11.548 
11.932 

32 

30.886 

29.974 

29.358 

27.090 

23.764 

22.384 

19.090 

12.317 

33 
34 

31.852 
32.816 

30.910 
31.846 

30.276 
31.194 

27.936 

28.784 

24.508 
25.250 

23.084 
23.784 

19.687 
20.282 

12.702 
13.087 

35 
36 

33.782 
34.746 

32.784 
33.720 

32.110 
33.028 

29.630 
30.476 

25.992 
26.736 

24.484 
25.182 

20.880 
21.476 

13.472 
13.857 

37 

35.712 

34.656 

33.946 

31.322 

27.478 

25.882 

22.072 

14.242 

38 
39 

36.678 
37.642 

35.594 
36.530 

34.864 
35.780 

32.170 
33.016 

28.220 
28.964 

26.582 

27.282 

22.670 
23.266 

14.627 
15.012 

MEAN  PRESSURE. 


161 


TABLE    XLVII. 

Mean  Pressure  of  Expanding  Steam. 

Absolute 
steal  n 
pressure. 

P 

1.333 
I 

On 

1.5 
Stea 
I 

de  of  expi 
1.6 
m  cut  off 
1 

MM.  Ill  Of 

2 
*t  I,  from 
} 

stc.-iin.  de 
2.666 
beginnin 
1      . 

loted  by  3 
3 
j  of  strok 
i 

L 

4 

B. 
| 

8 
i 

50 
55 

48.262 
53.088 

4i;.s:;.-> 
51.518 

45.875 
50.462 

42.328 
46.561 

37.133 
40.846 

34.977 
38.474 

•2'J.H'JS 
32.811 

19.246 
21.170 

60 

57.914 

56.202 

55.050 

50.794 

44.559 

41.972 

35.794 

23.095 

65 

70 

62.740 
67.566 

60.885 
65.569 

59.637 
64.225 

55.027 
59.260 

48.273 
51.986 

45.470 

48.967 

38.777 
41.760 

25.020 
26.944 

75 

80 

85 

72.:«):J 
77.216 
82.042 

70.252 
74.936 
79.619 

68.812 
73.400 
77.987 

63.493 
67.726 
71.959 

55.700 
59.413 
63.126 

52.465 
55.963 
59.461 

44.743 

47.726 
50.709 

28.869 
30.794  ; 
32.718 

90 
95 

86.866 
91.699 

85.303 
89.986 

82.574 
87.163 

76.192 
80.425 

66.840 
70.553 

62.958 
66.456 

53.692 
56.675 

34.643  i 
36.568  ! 

,  100 
105 

96.524 
101.35 

93.670 
98.353 

91.750 
S6.337 

84.657 
88.890 

74.267 
77.981 

69.954 
73.451 

59.657 
62.640 

38.493 
40.417 

110 

106.17 

103.04 

100.92 

93.123 

81.694 

76.949 

65.622 

42.342 

115 
120 

111.00 
115.83 

107.72 
112.40 

105.51 
110.10 

97.356 
101.59 

85.407 
89.121 

80.447 
83.944 

68.606 
71.589 

44.267 
46.191 

125 
130 

120.65 
125.48 

117.08 
121.77 

114.68 
119.27 

105.82 
110.05 

92.834 
96.548 

87.442 
90.940 

74.572 
77.555 

48.116 
50.041 

135 

130.30 

126.45 

123.86 

114.28 

100.26 

94.437 

80.538 

51.966 

140 
145 

135.13 
139.96 

131.13 
135.82 

128.45 
133.03 

118.52 
122.75 

103.97 
107.68 

97.935 
101.43 

83.520 
86.502 

53.890 
55.815 

150 
155 

144.78 
149.60 

140.50 
145.18 

137.62 
142.20 

126.98 
131.22 

111.40 
115.11 

104.93 
108.42 

89.485 
92.468 

57.739 
59.663 

160 

154.43 

149.87 

146.79 

135.45 

118.82 

111.92 

95.451 

61.588 

165 

170 

159.26 
164.08 

154.55 
159.23 

151.38 
155.97 

139.68 
143.92 

122.54 
126.25 

115.42 
118.92 

98.434 
101.41 

63.513 
65.437 

175 
180 

168.91 
173.73 

1  (53.02 
168.60 

160.55 
165.14 

148.15 
152.38 

129.96 
133.68 

122.42 
125.91 

104.40 
107.38 

67.362 
69.287 

185 

178.56 

173.28 

169.73 

156.61 

137.39 

129.41 

110.36 

71.212 

190 
195 

183.39 
188.21 

177.97 
182.65 

174.32 
178.90 

160.85 
165.08 

141.10 
144.82 

132.91 
136.41 

113.35 
116.33 

73.136 
75.061 

200 
210 

193.04 
202.69 

187.34 
196.71 

1X:!..->0 
192.68 

169.31 

177.78 

148.53 
155.96 

139.91 
146.90 

119.31 
125.27 

76.986 
80.835 

220 

212.34 

205.08 

201.85 

186.25 

163.39 

153.90 

131.24 

84.684 

230 
240 

221.99 
231.65 

241.30 
250.96 

215.45 
224.81 

211.03 
220.20 

194.71 
203.18 

170.82 
178.23 

160.89 
167.89 

137.20 
143.17 

88.534 
92.383 

250 
260 

234.18 
243.55 

229.38 
238.55 

211.H4 
220.11 

185.67 
193.18 

174.88 

181.88 

149.13 
155.11 

96.232 
100.08 

270 

260.61 

252.91 

247.73 

228.57 

200.52 

188.87 

161.07 

103.93 

280 
300 

270.26 
289.56 

262.28 
281.00 

256.90 
275.24 

237.04 
253.96 

207.95 
222.80 

195.87 
209.86 

167.04 
178.97 

107.78 
115.48 

1C2  STEAM  ENGINEERING. 

STRENGTH  OF   SPHERICAL,   SHELLS  OF 

STEAM-BOILERS.— Addendum  to  §  86,  page  105. 

§  126.  For  a  spherical  shell  the  tension  or  strain  is  equal  to  the  area 
of  the  great  circle  in  square  inches  multiplied  by  the  steam  pressure 
per  square  inch,  which  is  resisted  by  the  section  of  the  shell  in  the 
great  circumference. 

When  only  a  part  of  the  sphere  is  used,  like  in  spherical  ends  of 
boilers  or  steam-drums,  the  same  rule  holds  good,  only  that  the 
strength  must  be  calculated  for  the  whole  sphere. 

R  =  radius  of  the  sphere  in  inches. 
p  =  steam  pressure  in  pounds  per  square  inch. 
t  =  thickness  of  shell  in  fraction  of  an  inch. 
S  =  ultimate  strength  of  the  iron  in  pounds  per  square  inch. 

Action  of  steam, pit R?  =  St2K R,  the  reaction  of  the  shell. 
Ultimate  Strength  of  Solid  Shell  in  the  Sphere  without  Riveted  Joints. 

Steam  pressure,  p  = 1 

R 

f\  i  O 

Radius  of  sphere,  R  =  — 2 

Thickness  of  shell,  *  =  ^.       .        .        .        .        .3 

2  S 

Breaking-strain,  S— — *- 4 

Example  1.  The  spherical  end  of  a  boiler  is  made  of  iron  stamped 
S  =  60,000  and  t  =  0.25  of  an  inch  thick  in  one  sheet  without  joints. 
What  steam  bursting-pressure  can  that  spherical  end  stand  with  a 
radius  of  curvature  R  =  96  inches  ? 

2x0.25x60000     , 
Steam-pressure,        p  =  —    —  =  312.5  pounds. 

yt) 

These  formulas  are  the  same  as  those  for  cylindrical  shells,  with 
the  exception  that  the  radius  R  of  the  sphere  takes  the  place  for  the 
diameter  D  of  the  cylinder.  Therefore  a  sphere  is  double  as  strong 
as  a  cylinder  of  the  same  diameter.  The  coefficient  X  for  safety 
strength  will  therefore  be  the  same  .as  for  cylindrical  shells,  §  86, 
page  105,  namely, 


SPHERICAL  BOILER-ENDS. 


163 


TABLE  XXVI. 
Coefficients  A'  for  Spherical  Ends. 


Construction  of  Shell. 

X 

Per  cent, 
of  strength. 

Solid  plate  without  joints  

0.5 

100 

Double-riveted  drilled  holes 

04 

80 

Double-riveted  punched  holes  

0.35 

70 

Single-riveted  drilled  holes  

0.3 

60 

Single-riveted  punched  holes  

0.25 

50 

Steam-pressure, 
Radius  of  shell, 
Thickness  of  plate, 


p  = 


XtS 
R 

XtS 


.    5 


Breaking-strain, 


.    8 


The  radius  E,  of  the  spherical  end,  is  independent  of  the  diameter 
Z),  of  the  boiler  or  steam-drum. 

Example  6.  What  radius  is  required  for  a  spherical  boiler-end  of 
solid  plate  £  =  0.3  of  an  inch  thick  and  stamped  S  =  64,000  to  bear 
with  safety  a  steam-pressure  of  p  =  80  pounds  per  square  inch  ? 


Radius, 


0.5x0.3x64000 
80 


120  inches. 


Example  7.  The  iron  for  a  spherical  boiler-end  is  expected  to  bear 
S=  56,000  pounds  to  the  square  inch  of  section,  is  to  be  curved  to  a 
radius  R  =  84  inches,  and  to  have  one  double-riveted  lap-joint  with 
punched  holes,  and  to  bear  a  steam-pressure  of  p  =  96  pounds  to  the 
square  inch.  Required  the  thickness  of  the  iron? 


Thickness, 


84x96 
0.35x56000 


=  0.411  of  an  inch. 


164  STEAM  ENGINEERING  . 

PHYSICAL    PROPERTIES    OF    DIFFERENT 
KINDS    OF    VAPORS. 

§  127.  The  following  Table  48  shows  the  relation  between  temper- 
ature and  pressure  of  vapors  composed  of  the  four  principal  simple  ele- 
ments —  namely,  oxygen,  nitrogen,  hydrogen  and  carbon.  The  table  is 
deduced  from  the  experiments  of  Regnault,  except  the  column  for  car- 
bonic acid,  which  is  deduced  from  the  experiments  of  Faraday  and 
Pelouze;  but  those  experimenters  are  not  responsible  for  the  formulas 
and  tables  which  the  writer  has  deduced  from  their  experiments. 

The  vapors  of  water  and  carbonic  acid  have  been  treated  in  the  pre- 
ceding pages,  and  the  next  in  order  in  the  table  is  turpentine. 

Oil  of  Turpentine  is  distilled  from  resin  of  pine  trees.  It  is  a  vola- 
tile spirit  composed  of  Cw  HW,  and  boils  under  atmospheric  pressure 
at  a  temperature  of  338°  Fahr.  The  table  gives  the  pressure  under 
which  it  boils  at  different  temperatures. 

The  formulas  for  pressure  and  temperatures  of  turpentine  vapor  are 

T=281V6P-115. 


281 

Turpentine  is  a  transparent  liquid  or  gas  insoluble  in  water,  but 
dissolves  paints  and  many  gums  and  resins. 

Alcohol.  —  Pure  alcohol,  CtH602,  boils  under  atmospheric  pressure 
at  a  temperature  of  173°  Fahr.  The  formulas  for  pressure  and  tem- 
perature of  alcoholic  vapor  are 

T=l80yT-  108.        .        .        .        .1 


The  ideal  zero  of  vapor  of  alcohol,  according  to  the  formula,  should 
be  -108°  below  Fahr.  zero. 

The  pressure  of  vapor  of  alcohol  is  about  double  that  of  steam 
of  equal  temperature,  as  will  be  seen  in  the  Table.  The  vapor  of 
alcohol  has  been  tried  in  France  as  motive  power,  and  a  large  pas- 
senger steamer  named  "  Kabyl,"  built  in  the  year  1857,  was  supplied 
with  engines  and  boilers  for  the  use  of  alcohol  instead  of  water.  The 


PROPERTIES  OF  DIFFERENT  KINDS  OF  VAPORS.      165 

"  Kabyl "  was  running  from  Marseilles  to  ports  in  the  Mediterranean 
in  the  year  1858  with  partial  success,  but  the  alcohol  was  finally 
abandoned  for  the  reason  that  its  saving  in  fuel  did  not  compensate  for 
the  leakage  of  the  more  expensive  fluid. 

The  vapor  of  the  alcohol  was  condensed  in  an  ordinary  tubular 
fresh-water  condenser  and  returned  to  the  boiler,  thus  used  over  again 
perpetually. 

The  difficulty  appeared  to  be  the  leakage  of  alcohol,  and  conse- 
quently the  expense  of  supplying  that  fluid.  The  writer  was  on  board 
the  "  Kabyl "  during  the  first  trial  trip,  but  the  memorandum  then 
made  has  been  lost.  The  first  trial  was  made  with  ether,  which  was 
gradually  converted  into  alcohol — that  is,  one  atom  of  oxygen  and  one 
of  hydrogen  formed  water — but  even  with  this  change  in  the  fluid  the 
consumption  of  fuel  proved  to  be  very  economical. 

One  great  advantage  in  using  alcohol  or  ether  instead  of  water  in 
steam-boilers  is  that  no  incrustation  is  formed. 

>  There  was  a  very  strong,  but  rather  pleasant,  odor  of  alcohol  all 
over  the  ship,  of  which  the  passengers  did  not  seem  to  complain. 

Ether. — Pure  ether,  C4HbO,  boils  under  atmospheric  pressure  at  a 
temperature  of  97°  Fahr.  The  pressure  of  vapor  of  ether  is  five  to 
six  times  that  of  steam  of  equal  temperature,  as  seen  in  the  accom- 
panying table. 

The  formulas  for  pressure  and  temperature  of  etheric  vapor  are 

T=200v/P-216 1 


The  ideal  zero  is  -  216°. 

Benzine  is  a  transparent  liquid  insoluble  in  water  and  dissolves 
fatty  matter.  It  boils  under  atmospheric  pressure  at  a  temperature  of 
185°  Fahr. 

The  following  Table  L.  shows  the  boiling  point  of  benzine  under 
different  pressures. 

The  formulas  for  pressure  and  temperature  of  vapor  of  benzine  are 

T  =  2221//P-162 1 


166  STEAM  ENGINEERING. 


Ammonia,  N  H3,  is  a  colorless  vapor  or  liquid  which  boils  under 
atmospheric  pressure  at  about  -  19.3°  below  Fahr.  zero.  The  specific 
gravity  of  the  liquid  is  about  0.76,  and  according  to  Faraday's  ex- 
periments, freezes  to  a  white  transparent  solid  at  -  103°  Fahr.,  at 
which  temperature  the  pressure  of  its  vapor  is  about  5  pounds  to  the 
square  inch.  Ammonia  is  soluble  in  water,  with  which  it  generates 
heat,  forming  aqueous  ammonia  of  great  expansibility. 

The  high  tension  of  ammonia  at  low  temperatures  is  made  use  of  in 
producing  cold,  for  which  purpose  liquid  ammonia  is  kept  under  very 
high  pressure  in  a  vessel,  from  which  a  small  quantity  is  allowed  to 
gradually  escape  into  another  vessel  or  tube,  where  it  instantly  evap- 
orates, and  the  heat  absorbed  by  that  evaporation  produces  a  very 
low  temperature  of  the  surrounding  vessel  or  tube,  so  that  water  in 
the  neighborhood  will  freeze  to  ice.  This  is  the  principle  upon  which 
ice-machines  are  constructed. 

The  formulas  for  pressure  and  temperature  of  vapor  of  ammonia  are 


Protoxide  of  Nitrogen,  NO.  This  vapor  is  also  called  nitrous 
oxide  or  laughing  gas,  from  its  peculiar  effect  upon  the  mind  when 
inhaled. 

The  specific  gravity  of  nitrous  oxide  is  1.524. 

The  formulas  for  pressure  and  temperature  of  protoxide  of  nitro- 
gen are 

T=175l/P~-464  .....     1 


The  last  column  in  the  table  shows  the  pressure  per  square  inch  of 
nitrous  oxide,  corresponding  to  the  temperatures  in  the  first  columns. 

The  Roman  numbers  in  the  table  are  converted  from  Regnault's 
experiments,*  and  the  Italic  numbers  are  calculated  by  the  respective 
formulas. 

The  object  in  giving  this  table  is  to  show  at  a  glance  the  widely 
different  physical  properties  of  vapors  composed  of  only  oxygen,  nitro- 
gen, hydrogen  and  carbon. 

*  Memoires  de  1'Academie  de  France,  Tome  XXVI. 


PHYSICAL  PROPERTIES  OF   VAPORS. 


167 


TABLE  XLVIII. 

Temperature  and  Pressure  in  Pounds  per  Square  Inch 

of  Different  Kinds  of  Vapor. 

Tempe 
Cent. 

•atures. 
Fahr. 

Water, 
Steam. 

Carbonic 
acid. 

Turpen- 
tine. 

Alcohol. 

Ether 
of 
alcohol. 

Ben- 
zene. 

Ammo- 
nia. 

Protoxide 
of 
nitrogen. 

T 

T 

HO 

C02 

CioHia 

C4HeO, 

C4H50 

Ci2H6 

NH3 

NO 

—40 

40 

164.8 

0.464 

8.4 

202 

—35 

—31 

193.4 

0.626 

12.0 

246 

30 

22 

0.007 

225.7 

0.833 

0.025 

16.72 

270 

—25 

13 

0.012 

261.8 

1.092 

0.049 

2L4 

304 

20 

4 

0.18 

302.1 

0.064 

1.33 

0.112 

26.9 

340 

—15 

+  5 

0.027 

346.9 

0.098 

l!73 

0.17 

33.6 

381 

—  10 

14 

0040 

396.5 

0.125 

222 

0.25 

41.6 

425 

—  5 

23 

0.060 

451.2 



0.176 

2.82 

0.355 

50.8 

476 

0 

32 

0.089 

514.5 

6.64" 

0.245 

357 

0.489 

61.6 

530 

+  5 

41 

0.127 

577.4 

0.047 

0.341 

4.47 

0.66 

74. 

591 

10 

50 

0.177 

649.6 

0.057 

0.469 

5.54 

0.875 

88.4 

658 

15 

59 

0.246 

735.0 

0.069 

0.638 

6.84 

1.14 

105. 

732 

20 

68 

0.337 

814.2 

0.086 

0.859 

8.37 

1.46 

123.2 

813 

25 

77 

0.456 

886.6 

0.105 

1.15 

10.2 

1.85 

145 

903 

30 

86 

0.61 

1008 

0.133 

1.517 

12.27 

2.33 

168 

1000 

35 

95 

0.808 

1117 

0.151 

2. 

14.7 

2.89 

195 

1110 

40 

104 

1.06 

1234 

0.208 

2.583 

17.55 

3.55 

223.8 

1225 

45 

113 

1.38 

1362 

0.257 

3.33 

20.8 

4.34 

258 

1300 

50 

122 

1.78 

1471 

0.328 

4.25 

24.42 

5.24 

293 

1400 

55 

131 

2.27 

1644 

0.405 

5.38 

28.7 

6.3 

333 

1520 

60 

140 

2.88 

1817 

0.511 

6.78 

33.33 

7.54 

376.5 

1686 

65 

149 

3.61 

1968 

0.631 

8.44 

38.7 

8.97 

425 

1838 

70 

158 

4.51 

2147 

0.785 

10.45 

45.4 

10.6 

476 

2018 

75 

167 

5.58 

2352 

0.958 

12.9 

51.2 

12.4 

534 

2231 

80 

176 

6.86 

2542 

1.183 

15.71 

58.4 

14.65 

596 

2403 

85 

185 

8.37 

2758 

1.451 

19.1 

66.5 

16.9 

664 

2607 

90 

194 

10.2 

2988 

1.75 

23. 

75.3 

19.6 

736 

2825 

95 

203 

12.26 

32S2 

2.123 

27.6 

77.4 

22.6 

816 

3082 

100 

212 

14.7 

3500 

2.54 

32.8 

95.8 

26. 

900 

3359 

105 

221 

17.5 

3770 

3.00 

38.9 

108 

29.7 

1008 

3627 

110 

230 

20.8 

4060 

3.59 

45.75 

120 

33.7 

1135 

3926 

115 

239 

24.5 

4369 

4.22 

53.6 

134 

38.2 

1268 

4220 

120 

248 

28.8 

4695 

4.76 

62.6 

149.3 

43.2 

1425 

4558 

125 

257 

33.8 

5026 

4.86 

72.4 

165 

48.7 

1572 

4926 

130 

266 

39.3 

5394 

6.73 

83.6 

194 

54.6 

1745 

5272 

135 

275 

45.5 

5769 

7.85 

96. 

218 

61. 

1934 

5727 

140 

284 

52.5 

6165 

8.97 

109.9 

245 

66. 

2143 

6087 

145 

293 

69.3 

6586 

10.35 

125. 

270 

75.7 

2364 

6590 

150 

302 

79. 

7015 

11.7 

14L5 

300 

83.8 

2607 

7061 

155 

311 

79. 

7470 

13.25 

159.8 

335 

88.1 

2879 

7556 

160 

320 

90. 

7984 

15. 

187.1 

354 

96.7 

3156 

8128 

165 

329 

102. 

8462 

16.9 

214.3 

409 

105.9 

3481 

8710 

170 

338 

115.5 

9000 

18.9 

245.6 

451 

115.8 

3798 

9253 

175 

347 

130. 

9552 

21. 

283.4 

497 

126.2 

4157 

9914 

180 

356 

146. 

23.4 

320 

547 

137.4 

4545 

185 

365 

163.5 

25.9 

360 

601 

149.3 

4962 

190 

374 

183. 

28.5 

401 

659 

162.0 

5411 

195 

383 

203.5 

31.3 

443 

722 

175.5 

5892 

200 

392 

226. 

34.2 

490 

789 

189. 

6444 

168  DISTILLATION  OF  PETROLEUM  OILS. 

|  128.  BOILING  POINT  UNDER  ATMOSPHERIC  PRESSURE. 

V'1477~=  1.565. 

Water,  T  =  200j>  1477  -  101  =  +  21  2°. 

Carbonic  acid,  T=  61.404^1477  -  260  =  -  140°. 

Turpentine,  T=  281^/1477  -  115  =  +  324.7°. 

Alcohol,  T=  180^1477  -  108  =  +173.7°. 

Ether,  T=  200^/1477  -  216  =  4-  97°. 

Benzine,  T  =  222  ^14J  -  162  =  +  185.4°. 

Ammonia,  T=  150^1477  -  254  =  -  19.3°. 

Protoxide  of  nitrogen,    T  =  ITSjMiJ  -  464  =  -  190.2°. 

BOILING  POINT  OR  TEMPERATURE  OF  DISTILLATION  OF 
PETROLEUM  OILS. 

§  129.  The  variety  of  oils  distilled  from  petroleum  boil  at  widely 
different  temperatures,  according  to  their  specific  gravity.  The  boil- 
ing point  under  atmospheric  pressure  varies,  as  the  cube  of  the  specific 
gravity,  from  the  ideal  zero  -  215°  Fahr. 

S  =  specific  gravity  of  the  oil  compared  with  water  as  1  at  32°. 

T=  temperature  Fahr.  at  which  the  oil  boils  or  distills  under  atmo- 
spheric pressure. 

Boiling  point,  T=  1150  S3-  215°.         .     1 

81  f^  2]  5°' 

Specific  gravity,  S  =      ~~-      •        •     2 


Example  1.  The  specific  gravity  of  Kerosene  oil  is  0.808.  Required 
its  boiling  point  ? 

T=  1150  x  0.8083  -  215°  =  491.63. 

TEMPERATURE   OF   INFLAMMATION    OF   OILS   DISTILLED   FROM 
PETROLEUM. 

§  130.  The  volatility  of  distilled  petroleum  oils  under  atmospheric 
pressure  ceases  to  exist  under  a  certain  temperature  depending  upon 
the  sixth  power  of  the  specific  gravity  of  the  oil.  Above  that  tem- 
perature the  oil  evaporates  and  mixes  with  the  air,  and  can  be  ignited 
by  a  lighted  match. 


PROPERTIES  OF  PETROLEUM  OILS. 


169 


t  =  lowest  temperature  of  inflammation,  Fahr. 
S  =  specific  gravity  of  the  oil,  water  =  1. 

t  =  1200  S6- 140°. 


1200 


.     4 


Undistilled  or  mixed  oils  will  ignite  at  a  lower  temperature  than 
this  formula.  Crude  petroleum  ignites  at  60°. 

Example  3.  Required  the  lowest  temperature  of  inflammation  of 
Kerosene  oil  of  specific  gravity  0.805  ? 

t  =  1200  x  0.8058  -  140  =  180°. 


TABLE  L. 

Temperatures  of  Distillation  and  Inflammation  of  Petroleum 
Oils. 


Sp.  Kr. 

S 

Names  of  Petroleum  Oils. 

Dist 
Fahr. 

illation. 
Cent. 

Inflam 
Fahr. 

mation. 
Cent. 

0.6000 
0.6125 
0.625 
0.6375 
0.6500 
0.6625 
0.675 
0.6875 
0.7000 
0.7125 
0.7250 
0.7375 
0.7500 
0.7625 
0.7750 
0.7875 
0.8000 
0.8125 
0.8250 
0.8375 
0.850 
0.8625 
0.8750 
0.8875 
0.9000 

34° 
49 
63 
83 
101 
119 
139 
159 
180 
201 
219 
246 
270 
295 
320 
347 
375 
402 
424 
460 
490 
524 
555 
589 
623 

1.11° 
9.44 
17.22 
28.33 
38.33 
48.33 
59.44 
70.55 
82.22 
93.88 
103.8 
118.8 
132.2 
146.1 
160.0 
187.7 
190.5 
205.5 
217.7 
237.7 
254.4 
273.3 
290 
304.4 
328.3 

-84° 
-76 
-68 
-59 
-49 
-38 
-26 
-13 
2 
18 
35 
54 
74 
97 
121 
142 
176 
207 
240 
276 
314 
356 
399 
447 
498 

-65° 
-60 
-55 
-51 
-45 
-39 
-32 
-25 
-16 
7.7 

Amvlene  

Gasolene  

Toluene  

-t-1.66 
12.2 
23.3 
36.15 
49.4 
61.1 
79.4 
97.2 
115 
135 
156 
180 
204 
230 
259 

Naphtha  

Naphtha  or  Pvridine  

Lutidine  

Paraffine 

Mineral  Sperm  Oil  

Lubricating  Oil 

APPENDIX. 


TECHNICAL  TERMS  IN  MECHANICS. 

THE  science  of  Mechanics  has  heretofore  been  afflicted  with  a  lan- 
guage of  vague  terms  promiscuously  used  without  definite  meaning,  so 
that  different  ideas  have  been  formed  from  one  and  the  same  expres- 
sion and  a  variety  of  terms  have  been  employed  to  express  one  and 
the  same  principle. 

The  most  crucial  test  of  perfection  of  a  science  is  precision  in  its 
vocabulary  and  perspicuity  in  its  principles,  so  that  each  expression 
bears  a  definite  meaning. 

The  writer  has  for  many  years  labored  upon  this  subject — namely, 
to  expel  some  indefinite  terms  and  expressions  which  have  heretofore 
embarrassed  the  science  of  Mechanics.  In  discussing  the  subject  he 
has  encountered  difficulties  with  learned  men,  many  of  whom  appear 
to  have  only  faith  in  the  old  dogmas,  and  have  thus  thrown  obstacles 
in  the  way  of  success. 

Mr.  William  Dennison  of  East  Cambridge,  Mass.,  was  the  first  one 
who  understood  and  acknowledged  the  correctness  of  the  new  classifica- 
tion of  dynamic  elements  and  functions,  and  of  their  respective  defini- 
tions. Mr.  Dennisou  addressed  the  author  on  the  subject  as  follows : 

EAST  CAMBRIDGE,  MASS.,  May  12, 1874. 
MR.  JOHN  W.  NYSTROM, 

Dear  Sir — In  reading  your  pamphlet  on  Dynamics  I  have  been 
greatly  interested,  as  I  always  am  on  all  such  subjects ;  .but  this  sub- 
ject should  interest  every  one  especially  until  its  proper  terms  be 
adopted  and  their  meaning  permanently  established.  Except  among 
mechanics  you  will  seldom  find  any  two  persons  to  have  the  same 
ideas  upon  this  subject,  notwithstanding  assertions  to  the  contrary. 

The  very  fact  that  the  simple  question  of  force  of  a  falling  body 
was  discussed  by  so  many  learned  men,  all  with  different  ideas  on  the 
subject,  and  no  two  of  them  agreed  as  to  which  is  right,  is  sufficient 
proof  of  ths  present  confusion  in  Dynamics, 
iro 


DENNISON'S  COMMENTS.  171 


Your  reply  to  these  jarring  opinions,  as  well  as  to  all  other 
tions  in  the  pamphlet,  is  forcible,  correct  and  to  the  purpose. 

I  consider  the  basis  upon  which  you  have  placed  this  subject  to  be 
firm  and  well  constructed,  and  of  such  a  nature  as  never  to  be  over- 
thrown or  destroyed. 

You  have  also  succeeded  admirably  in  placing  the  subject  in  the 
most  clear,  comprehensive  and  proper  light. 

Had  there  been  such  a  treatise  in  our  schooldays,  it  would  have 
been  of  the  greatest  assistance  to  us  all,  then  and  since.  But  this  sub- 
ject has  always  been  in  such  a  state  of  confounded  conglomeration 
that  we  have  been  obliged  to  rely  upon  our  own  reasoning  powers 
and  practical  understanding ;  therefore  but  few  comparatively  have 
been  able  to  master  the  subject. 

I  have  often  been  impressed  with  the  idea  that  some  scientific  men 
like  to  nourish  high-sounding  terms,  such  as  those  you  have  rejected 
as  useless  and  confusing.  They  often  display  extraordinary  ability  in 
Compiling  highly  scientific  terms  into  heaps  of  phrases  which  may  ap- 
pear learned  to  those  not  familiar  with  the  subject,  whilst  they  are 
sometimes  mere  inventions  of  words  pretending  to  represent  myste- 
rious phenomena.  Yours  truly, 

WILLIAM  DENNISON. 

In  a  pamphlet  on  dynamical  terms  the  writer  invited  institutions 
of  learning  to  discuss  the  subject,  which  invitation  was  accepted  by 
many,  of  which  a  few  sided  with  the  writer ;  but  the  majority  were 
against  his  views.  The  response  of  Professor  Gustav  Schmidt,  of  the 
Polytechnic  Institute  at  Prague,  in  Bohemia,  may  serve  as  an  average 
illustration  of  the  present  condition  of  the  science  of  Mechanics  in 
institutions  of  learning.  The  ideas  on  the  subject  held  by  others  are 
substantially  the  same  as  those  of  Prof.  Schmidt. 

In  the  following  pages,  the  comments  of  Prof.  Schmidt  are  on  the 
left-hand  and  the  answers  on  the  right-hand  pages,  so  that  the  num- 
bers of  the  paragraphs  of  the  comments  correspond  to  the  numbers  of 
the  answering  paragraphs. 

The  division  into  paragraphs  has  been  made  by  the  author. 


172  PROFESSOR  SCHMIDT'S  COMMENTS. 

(Translation  from  the  German.) 

MR.  JOHN  W.  NYSTROM, 

Dear  Sir  —  It  affords  me  great  pleasure  to  comply  with  your  request 
for  a  written  opinion  on  your  work,  "  Principles  of  Dynamics,"  and 
will  do  so  in  German  on  account  of  my  insufficient  knowledge  of  the 
English  language. 

§  1.  I  have  no  objection  to  your  answering  me  publicly  in  an 
American  journal,  provided  you  would  publish  an  idiomatic  transla- 
tion of  this  letter. 

§  2.  The  term  "  Pferde-kraft  "  (horse-power)  has  become  obsolete  in 
Germany,  and  has  been  replaced  by  the  term  "  Pferde-starke"  (horse- 

!£• 

strength),  as   proposed  by  Renleaux.      The  product    ^  =  F  V=  — 

should  consequently  be  called  horse-strength. 

§  3.  It  is  customary,  however,  to  use  the  word  "  effect,"  but  not  the 
word  "kraft"  (force),  as  under  no  circumstance  would  it  answer  for 
the  German  idiom  to  use  the  term  "kraft"  (power)  for  "effect"  or 
"  pferde-starke  "  (horse-strength  or  force). 

§4.  The  former  Prussian  "pferde-starke"  undoubtedly  had  513 
second  foot-pounds  or  480  foot-pounds  of  the  new  weight  ;  this,  how- 
ever, is  not  582,  but  544.8  English  second  foot-pounds. 

§5.  The  present  German  "  pferde-starke  "  has,  as  in  France,  75 
second-metre  kilogrammes  =  542.5  English  foot-pounds. 

§  6.  The  unit  proposed  by  you  —  namely,  500  English  foot-pounds  — 
would  be  69£,  or  nearly  70  metre  kilogrammes,  equal  to  the  perform- 
ance of  a  horse  at  the  plough. 

§  7.  As,  however,  the  English  measurement  will  probably  give  way 
to  that  of  the  French  during  this  century,  the  75  M.  K.  already 
adopted  will  most  probably  be  retained. 

§  8.  The  product  F  T  (dynamical  moment,  as  you  call  it)  is 
never  used.  It  could  have  a  meaning  only  if  the  force  F  remains 
constant  during  the  time  T;  then  most  certainly  for  a  uniformly  ac- 
celerated motion  from  a  state  of  rest,  F  T  would  be  =  M  V. 

§  9.  However,  for  a  uniformly  accelerated  motion  with  an  initial 
velocity  C,  F  T=  M  (  V-  (7)  ;  for  instance,  in  the  case  of  a  vertical 
projection 


,          then          W 

gT=C-V        and         V=C-gT. 


NYSTROM'S  ANSWER.  173 

PROFESSOR  GUSTAV  SCHMIDT, 

Dear  Sir  —  It  affords  me  great  pleasure  to  answer  your  comments 
on  my  "  Principles  of  Dynamics,"  and  I  hope  the  translation  of  your 
paper  from  German  to  English  is  satisfactory  to  you. 

§  1.  No  American  journal  would  publish  this  kind  of  discussion, 
for  which  reason  I  have  concluded  to  append  the  same  to  this  work 
on  "  Steam  Engineering." 

§  2.  Both  the  terms  "kraft"  and  "starke"  in  the  German  language 
mean  "  force."  You  have  no  German  word  for  the  function  ^  =  F  V, 
which  is  power.  Both  your  terms  for  horse-power  mean  horse-force. 
Strength  or  "starke"  is  the  capability  of  resisting  static  force. 

igr 
F  V=  —  is  power  in  effects. 

The  products 


The  term  "  Pferde-kraft  "  is  more  proper  than  "  Pferde-sterke." 

§  3.  You  say  it  is  customary  to  use  the  word  "effect"  and  give  the 
other  terms  for  which  it  is  not  used,  but  do  not  state  for  what  it  is 
used  or  what  are  its  constituent  elements.  The  term  "effect"  repre- 
sents a  unit  of  measurement  of  power  —  namely,  a  second  foot-pound 
of  power.  Horse-power  is  another  unit  of  power,  consisting  of  550 
effects.  You  do  not  distinguish  power  from  force  in  your  language. 

§  4.  According  to  the  data  of  Prussian  weight  and  measure  in  my 
possession—  namely,  1.0297  ft.  x  1.1023  Ibs.  x  513  =  582.18  English  foot- 
pounds. This,  however,  does  not  affect  the  correctness  of  the  princi- 
ples of  Dynamics. 

§  5.  I  gave  542.47  English  second  foot-pounds  per  75  second-metre 
kilogrammes,  and  did  not  know  the  new  Prussian  measures. 

§  6.  This  unit  was  proposed  only  to  accommodate  the  English 
weight  and  measure  for  the  easy  calculation  and  estimation  of  horse- 
power and  practice. 

§  7.  It  is  yet  doubtful  whether  the  English  measurement  will  give 
way  for  that  of  the  French  in  the  present  century,  of  which  only  24 
years  remain. 

§  8.  Because  the  momentum  F  Tis  not  used,  is  the  reason  why  con- 
fusion still  pervades  the  dynamics  of  matter.  This  momentum  is  there, 
whether  it  is  used  or  not.  When  F  is  the  mean  force  in  the  time  T, 
the  momentum  must  always  be  F  T=  M  V. 


174  PROFESSOR  SCHMIDT'S  COMMENTS. 

§  10.  For  a  variable  force  F,  however, 

Ffit  =  M  cv,  or 
„     ,,dv     W    6v         ,     8w       F 


§  11.  Only  this   equation  will  answer  for  a  general  application  ; 

M  V 

F=  -  (force  of  a  moving  body),  on  the  contrary,  is  quite  super- 

fluous and  inadmissible  idea,  as  T,  and  consequently  F,  would  be  en- 
tirely arbitrary. 

§  12.  You   entirely  omit  the  above-mentioned   highly  important 

f\  TTT 

term  g  =—-  =        which  is  the  acceleration. 
ct     M 

§  13.  For  "work"  in  a  moving  body,  JT=pf  V*  =  W~,  the  old 

9 

term  "  lebendigo-kraft,"  living  force,  also  sometimes  "  energie,"  en- 
ergy, is  used  in  Germany.  I  have  proposed  for  it  "  bervegungs 
arbeit,"  work  of  motion,  to  distinguish  it  from  "  verschriebungs 
arbeit,"  work  of  pushing  or  drawing,  F  S  or  universally  /  E  cs. 

§  14.  We  do  not  designate  the  value  ^MV1  "  Grosse  der  Berve- 
gung,"  Quantitat  der  Bervegung  (quantity  of  motion),  but  the  pro- 
duct MV  which  you  call  (Bervegungs  moment)  moment  of  motion. 

§  15.  You  reject  the  term  "acting  force"  and  "working  force." 
If,  however,  the  mass  M  is  moved  by  a  force  F,  which  is  exactly 
equal  to  the  sum  of  all  resistances  F',  and 
*te  velocity  V  is  consequently  invariable,  as, 
for  instance,  in  the  case  with  a  train  of 
cars,  then  F  is  a  "  working  force  "  produ- 
cing the  pushing  or  pulling  work  k  =  FS,  which  is  consumed  by  the 
equally  great  resistance  F'K'  =  F'S.  Therefore  the  force  F  cannot 
cause  any  acceleration  of  speed. 

If  the  force  F  is  greater  than  the  resistance  F',  then  there  remains 

W 
an  accelerating  force  f=F-F',  which  imparts  to  the  mass  M=  —  the 


f 

acceleration  g'  =  -==-r;  =  ~,  if  /  is  a  constant  quantity,  or  if  /  is  inva- 
^T    M 

r\qj[  f 

riable  it  imparts  the  acceleration  g'  =  —  —  =  —  .     This  accelerating 

ct      M 

force  f=F-F'  must  not  be   mistaken   for   a  non-accelerating  but 
"  working  force  "  F,  nor  for  a  non-working  but  only  "  deformirender  " 


NYSTROM'S  ANSWER.  175 

§  9.  Motion  and  rest  are  only  relative,  for  which  reason  the  velocity 
V  must  always  mean  the  difference  of  velocity  caused  by  the  action 
of  the  force  F  on  a  mass  free  to  move,  whether  accelerating  or  retard- 
ing. 

§  10.  There  is  nothing  in  my  treatise  on  Dynamics  which  contradicts 
your  mathematical  display.  You  will  find  these  formulas  in  my  "  Ele- 
ments of  Mechanics." 

§  11.  Your  professorship  is  not  invested  with  a  prerogative  to  admit 
or  dismiss  the  force  of  a  moving  body;  for  however  arbitrary  the  force 
and  time  may  be,  they  are  there,  in  defiance  of  your  opinion. 

§  12.  In  the  argument  referred  to  there  was  no  call  for  the  term 
you  say  I  omitted ;  you  will  find  that  term  in  my  "  Elements  of  Me- 
chanics." 

§  13.  I  hope  you  will  not  attempt  to  introduce  any  more  confusion 
m  Dynamics,  such  as  the  term  "  work  of  motion,"  which  indicates  that 
motion  is  a  function  consisting  of  work  and  something  else.  You 
have  not  defined  the  constituent  elements  of  motion. 

§  14.  I  do  not  designate  %  M  F2  as  "  quantity  of  motion,"  but  have 
rejected  that  term  in  dynamics.  Nor  should  the  term  "quantity  of 
motion  "  designate  the  momentum  M  V.  I  use  only  one  definite  term 
for  each  quantity  in  Dynamics,  but  you  do  not  appear  to  have  a  defi- 
nite dynamical  language. 

§  15.  The  term  "acting  force"  conveys  the  idea  that  there  may 
exist  forces  which  do  not  act.  The  simple  term  "force"  implies  that 
it  acts,  for  which  reason  I  proposed  to  reject  "  acting."  "  Motive 
force"  is  the  proper  term  for  your  illustration,  but  we  may  call  J^the 
acting  force  and  F-  F'  the  motive  force.  This  motive  force  may  be 
wholly  applied  against  the  friction  of  the  car  moving  with  a  uniform 
velocity  on  the  road,  or  a  part  of  it  may  be  expended  in  accelerating 
the  velocity  of  the  car.  It  is  not  wrong  to  add  the  verb  "acting"  to 
the  term  force,  but  I  only  proposed  to  reject  the  term  as  superfluous 
in  the  sense  in  which  it  is  often  used. 

All  your  forces  F  F'  and  /  are  "  acting  forces "  as  well  as  simple 
"  forces."  You  have  not  given  any  example  of  forces  which  do  not 
act.  It  is  necessary  in  Mechanics  to  distinguish  "motive  force"  from 
"  static  force,"  but  both  of  them  are  acting. 

The  purpose  for  which  a  force  is  applied  does  not  alter  the  nature 
of  that  force.  Deforming  force ! ! ! 


176  PROFESSOR  SCHMIDTS  COMMENTS. 

(deforming  or  pressing)  force.     That  it  must  not  be  confounded  with 
a  pull  or  a  pressure. 

§  16.  I  consider  T,  S,  F,  M  as  elements. 

or 

t  =         in    general 


K=FS 


Functions. 


9=—    «        «        9- f— 

Also,           the  mean  force  Fm  =  J  — - . 
Power,  ^  = •  =  jPm  Fm. 


§  17.  It  is  certainly  more  natural  to  consider  s  and  t  as  elements 
and  the  differential  quotient  V=  —  as  a  derived  equation  than  re- 


function. 


gard  t  and  V  as  elements  and  S=  \  Vf)t  as  a  derived 

§  18.  The  following  are  other  functions. 

The  acceleration  of  motion  by  the  accelerating  force, 


'    ~  M  ~dt  ~&e' 

§  19.  The  "  quantity  of  motion  "  =  M  F,  and  the  stored-up  "  working 

F2 
force  "  (living  force)  ^MV2  =  W  -  . 

§  20.  You  do  not  think  it  right  that  all  authorities  without  excep- 
tion should  consider  "  work  "  K=  (  F  6s  as  independent  of  time. 

You  will,  however,  most  surely  admit  that  in  a  finished  building 
there  is  contained  a  fixed  quantity  of  work,  to  do  which,  of  course, 
some,  but  an  indeterminate,  time  would  be  necessary. 

§  21.  Consequently  we  cannot  say  that  the  determinable  work  is  de- 
pendent on  the  indeterminable  time. 

§  22.  If  the  work  was  built  in  a  year,  it  has  been  done  "  in- 
tensely "  (intensive).  If  three  years  have  been  needed  for  the  same 
work,  then  it  has  been  done  with  "  less  intensity." 


NYSTROM'S  ANSWER.  177 

The  definition  of  a  physical  element  is,  an  essential  principle  which 
cannot  be  resolved  into  two  or  more  different  principles.  Therefore  an 
element  cannot  be  divided  by  an  element  and  the  quotient  become  a 
function,  as  appears  in  your  notions  of  elements  and  functions.  You 
say  time  and  space  are  elements,  and  then  divide  space  by  time  and 
say  the  quotient  is  a  function — velocity. 

o 

When  velocity  F= — ,  we  have  space  £=  V  T,  which  proves  that 

space  is  a  function  of  velocity  and  time. 

§  17.  Physical  facts  are  not  always  natural  to  the  mind.  There 
was  a  time  when  matter  was  supposed  to  consist  of  only  three  simple 
elements — namely,  air,  water  and  earth — which  was  natural  in  those 
days. 

§  18.  No,  sir.  These  quantities  are  neither  elements  nor  functions, 
for  they  only  express  the  numerical  ratio  of  force  and  mass. 

§  19.  This  has  been  commented  on  before.  Working  force  means 
motive  force.  There  is  no  living  force  in  a  dead  body. 

§  20.  Most  decidedly,  because  the  time  is  included  in  the  space 
$=  V  T.  I  admit  that  a  fixed  quantity  of  work  is  required  for  erect- 
ing a  building ;  but  when  you  add  the  time  necessary  for  it,  it  cannot 
be  independent  of  time.  If  the  building  can  be  erected  in  no  time, 
then  that  work  is  independent  of  time. 

§  21.  Work  does  not  bear  any  fixed  relation  between  its  elements, 

IB* 

but  the  product  F  V  T  is  work.     You  say,  §  2,  that  F  V-  — ,  from 

which  we  have  the  work  K=  F  V  T. 

§  22.  Here  you  introduce  a  new  term,  which  you  have  not  defined. 
Is  "intensity"  an  element  or  a  function?  If  a  function,  of  what  ele- 
ments is  "  intensity  "  composed  ? 

§  23.  In  this  case  your  formula  is  right,  but  your  argument  is 
wrong.  You  eliminate  the  time  from  the  work  in  order  to  get  the 
power.  By  the  term  "intensity"  you  mean  power,  and  from  your 
own  formula — 

§  24.  We  have  the  work  K=  %  T,  which  means  that  the  work  can 
be  accomplished  in  any  desired  length  of  time,  but  only  at  the  ex- 
pense of  power. 

§  25.  Such  is  the  case  with  the  locksmiths — namely,  that  one  worked 
with  double  the  power  of  the  other,  and  consequently  earned  double 
the  wages  in  equal  lengths  of  time. 

§  26.  Money  is  equivalent  to  work,  and  you  must  expend  F  V  T 
to  earn  it.  There  is  no  fixed  relation  between  Ft  V  and  T,  but  can 
12 


178  PROFESSOR  SCHMIDT'S  COMMENTS. 

§  23.  Not  the  work  but  the  "  intensity  of  the  work,"  the  "  arbeit- 

TT 

starke  "  (working-strength)  £  =       depends  on  the  time. 

§  24.  If  two  locksmiths  do  the  same  work,  the  one,  however,  in 
half  the  time  the  other  takes,  then  the  first  one  has  worked  with 
twice  the  intensity  the  other  did. 

§  25.  They  received  the  same  compensation  for  the  same  work, 
but  the  skillful  workman  received  double  the  wages  in  the  same  time 
because  his  "  arbeitstarke"  (working-strength)  was  double  as  great. 

§  26.  The  pay  per  piece  in  like  work  is  independent  of  time,  but 
the  resulting  earnings  per  day  are  in  direct  ratio  to  the  arbeitstarke 
(  working-stren  gth  ) . 

§  27.  The  following  function  may  be  derived  from  the  pay  per 
piece  L  and  from  the  time  used  per  piece  : 

Pay  in  a  unit  of  time  A  =  — . 

§  28.  According  to  your  idea,  on  the  contrary,  the  price  per  piece 
L  would  be  a  function  only  because  it  is  the  product  of  A  and  T, 
and  because  you  will  only  consider  a  product,  and  not  a  quotient,  as  a 
derived  function. 

§  29.  Such  a  confusion  of  ideas  as  is  the  case  in  all  the  articles 
concerning  "force  of  falling  bodies,"  especially  on  page  19  of  the 
Scientific  American  of  the  22d  of  June,  1872,  occurs  seldom  in  Ger- 
many. 

§  30.  There  does  not  exist  any  "force  of  falling  bodies,"  only  a 

F2 
"  bervegungs-arbeit "  (work  of  motion)  =  £  MV2=  W  — ,  stored  up 

in  the  falling  body,  equal  to  the  "  verschiebungs-arbeit "  (pushing 
or  pulling  work)  WS,  which  was  necessary  to  raise  the  weight  W  to 

F2 
a  height  S=  — . 

§  31.  This  stored-up  "external  work  of  motion"  is  then  changed 
into  "verschiebungs-arbeit"  (pushing  \vork~)  =Rs  as  a  mean  resist- 
ance, .R  has  been  overcome  through  the  distance  s.  Therefore  you 
state  correctly  that  ft  s=  WS.  But  E  is  not  the  force  of  the  falling 
body,  but  rather  the  resistance  of  the  down-pressing  body  through  the 
distance. 

§32.  Your  equation  14  K=FVT=^,  on  page  21  of  this 
treatise,  is  incorrect,  as  F  is  the  mean  velocity  and  F  the  initial  force. 


NYSTROM'S  ANSWER.  179 

vary  ad  libitum,  only  that  their  product  must  correspond  with  the 
money. 

What  you  call  "  strength  of  work,"  intensity,  or  "  working  strength  " 
is  power  f=FV. 

§  27.  The  pay  A  per  unit  of  time,  according  to  the  power  of  the 
workman,  may  be  expressed  as  follows : 

Wages,  ^  =  f=?. 

§  28.  I  have  distinguished  the  terms  "element"  and  "function"  by 
proper  definitions,  but  you  use  those  terms  promiscuously  according 
to  individual  caprice.  I  maintain  that  the  product  of  two  or  more 
elements  is  a  function,  and  that  a  quotient  is  a  solution  of  a  function. 

§  29.  The  confusions  you  allude  to  are  written  by  Dr.  Van  der 
Weyde  and  other  doctors  of  philosophy,  for  which  I  am  not  respon- 
sible. I  do  not  consider  your  ideas  of  Dynamics  to  be  much  better 
than  those  of  the  other  'professors  who  have  commented  upon  that 
subject. 

§  30.  Place  yourself  under  a  falling  body  and  let  it  strike  upon 
your  head;  and  if  you  experience  no  force,  then  there  is  no  force  in  a 
falling  body.  Please  let  me  hear  from  you  after  you  have  made  the 
experiment. 

§  31.  Is  the  external  work  of  motion  stored  upon  the  surface  of  the 
body?  The  pushing  work  must  then  be  the  internal  work,  which 
leaks  out  when  the  body  strikes  ? 

No  force  can  be  experienced  without  an  equal  amount  of  resistance, 
and  the  force  of  a  falling  body  is  equal  to  the  force  of  resistance  it 
meets  with. 

§  32.  Here  you  have  really  discovered  an  error  of  mine,  for  which 
I  am  glad  to  give  you  due  credit,  and  thank  you  for  calling  my  at- 
tention to  it.  My  idea  was  to  express  the  work  of  attraction  of  two 
bodies  very  far  apart  in  space  compared  with  the  distance  between 
their  centres  of  gravity  when  in  contact,  in  which  case  the  force  of 
attraction  varies  inversely  as  the  square  of  the  distance  between  the 
approaching  bodies.  Your  formulas  do  not  include  the  requisite  ele- 
ments for  that  work,  but  merely  give  the  work  of  a  falling  body  near 
the  surface  of  the  earth. 

M  and  m  =  masses  of  the  respective  bodies. 

D  =  distance  apart  in  feet  from  which  the  work  is  counted. 
d  =  any  shorter  distance  until  in  contact. 

<p  =  28693080,  coefficient  of  attraction. 


180  PROFESSOR  SCHMIDT'S  COMMENTS. 

If  W=  in,  g  is  the  weight  of  a  body  at  the  surface  of  the  earth  of  a 
radius  a,  then  the  attraction  of  gravity  for  the  distance  x  is 


and  the  work  IT  for  a  fall  from  the  height  »>  a  to  the  surface  of  the 
earth  will  be  K=  -p  Vx=-mg  a>**- 


a    x  x 


If  £  is  only  larger  than  a  by  a  very  small  quantity  h,  then  will 

a_     a  1        .     h  a _h 

—  =          =  -      -  —  1  or     1        =  — . 

x     a  +  x     1  +  h  a  x     a 


Therefore,  K=  W  a-  =  Wh,  our  well-known  equation. 


§  33.  All  German  professors  are  most  probably  of  the  opinion  that 
the  professor's  opinion  (page  4)  in  the  main  is  perfectly  correct,  and 
that  your  answer  is  composed  of  sophisms. 

§  34.  Willingly,  however,  do  I  acknowledge  as  commendable  your 
desire  to  arrive  at  a  determination  of  the  dynamical  terms,  and  to 
eradicate  all  superfluous  ones. 

§  35.  The  expression,  "  principle  of  conservation  of  force  "  (princip 
der  erhaltung  der  kraft),  is  a  very  unfortunate  one,  and  unhappily 
has  already  led  many  half-educated  persons  astray.  That  chosen  by 
Professor  Mach,  of  Prague,  is  more  correct — namely,  "  principle  of 
the  conversation  of  work"  (princip  der  erhaltung  der  arbeit) — and 
still  more  correct  would  be  "  principle  of  conversion  of  work." 

§  36.  I  therefore  say  there  are  four  kinds  of  work  which  are  intro- 
convertible. 

First.  External  pushing  or  pulling  work  (aussere  verschiebungs 
arbeit). 

Second.  External  work  of  motion  (aussere  bervegungs  arbeit). 


NYSTEOM'S  ANSWER.  181 


K=  work  of  attraction  in  foot-pounds,  in  drawing  the  bodies  together. 

Mm»d  Mm/I      1 

8Jr—       - 


This  formula  expresses  the  true  work  in  foot-pounds,  English 
measures. 

In  the  case  of  meteors  falling  on  the  surface  of  the  earth  we  may 
assume 

D  =  oo  and  —  =  0. 
D 

d  =  20,887,680  feet  radius  of  the  earth. 

M  =  402,735,000,000,000,000,000,000  matte,  mass  of  the  earth. 
m  =  mass  of  the  falling  meteor  expressed  in  matts. 
The  work  in  foot-pounds  of  a  meteor  striking  the  earth  will  then  be 

K=  671926000  m. 

For  very  small  meteors  the  greatest  part  of  this  work  may  be  con- 
verted into  heat  in  passing  through  the  atmosphere,  and  we  call  it 
shooting-stars. 

Assuming  the  mean  height  of  the  atmosphere  to  be  60158  feet,  the 
radius  of  the  atmospheric  sphere  is  20947018  feet  =  d. 

The  velocity  with  which  a  meteor  enters  the  atmosphere  will  then  be 

2  —  =  36607.46  feet  per  second. 
a 

§  33.  I  consider  it  doubtful  that  all,  or  even  a  majority,  and  noi 
one  of  the  German  professors  who  understood  the  subject,  would  be 
of  the  opinion  of  the  professor  in  question.  You  will  no  doubt  say 
that  my  answers  to  you  are  composed  of  sophisms,  but  I  can  stand 
that  easily,  being  accustomed  to  such  charges. 

§  34.  I  am  very  glad  that  you  consider  my  labor  commendable,  and 
would  state  my  acknowledgment  in  emphatic  tertfis  but  for  your  em- 
ployment of  such  a  conglomeration  of  dynamical  terms,  which  are  the 
worst  I  have  met  with. 

§  35.  These  terms  are  all  useless,  and  should  never  be  admitted  into 
any  school  or  any  text-book.  Work  in  dynamics  corresponds  to 
volume  in  geometry,  but  we  do  not  give  different  names  to  that 
volume  according  to  the  shape  of  the  space  it  occupies.  A  vessel 
holding  100  gallons  of  water  is  a  fixed  volume  independent  of  the 
shape  of  the  vessel.  If  the  vessel  is  cylindrical,  we  do  not  say  it  con- 


182  PROFESSOR  SCHMIDT'S  COMMENTS. 

Third.  Internal  pushing  or  pulling  work  at  work  of  pressure  (Inner 
verschiebunga  arbeit  oder  deformerings  arbeify. 

As,  for  instance,  in  the  bent  bow,  or  in  an  extended  or  compressed 
spring,  in  consequence  of  the  change  in  the  relative  position  of  the 
molecules,  which  is  against  the  molecular  forces.  In  permanent  gases 
this  is  infinitely  small,  and  in  condensible  vapors  it  is  also  very  small. 

Fourth.  Internal  work  of  motion  (Inner  berveguns  arbeit),  which 
appears  as  heat. 

Internal  (modicular)  work  of  motion  is  stored  up  in  a  compressed 
gas  or  vapor,  which  can  partly  change  itself  into  external  pushing  or 
pulling  work. 

§  37.  There  is  likewise  internal  work  of  motion  stored  in  hot  gases, 
the  products  of  combustion,  which  is  transmitted  to  the  water  by  the 
heating  surface  of  the  steam-boiler,  and  then  changes  itself  into  the 
internal  pushing  or  pulling  force,  which  must  be  furnished  for  the 
tearing  asunder  of  the  molecules  of  water,  and  changes  also  into  in- 
ternal work  of  motion,  which  the  now  generated  molecules  of  steam 


§  38.  In  forging,  rolling,  drilling,  planing,  etc.,  the  greatest  part 
of  the  work  is  changed  into  internal  work  of  motion  (heat). 

§  40.  Hoping  that  you  will  not  take  my  frank  remarks  on  your 
work  in  an  unfriendly  manner,  I  subscribe  myself 

Yours  respectfully, 

GUSTAV  SCHMIDT, 

Professor  of  Technical  Mechanics  and  of  Theoretical  Mechanical 
Engineering  at  the  K.  K.  German  Polytechnic  Institute  of  the  King- 
dom of  Bohemia,  Austria. 

PRAGUE,  July  1,  1875. 

The  translation  of  Professor  Schmidt's  papers  was  made  by 
Mr.  P.  PISTOR  of  Philadelphia. 


From  the  foregoing  discussion  it  is  clear  that  the  subject  of  Dy- 
namics lacks  perspicuity  in  the  German  language  for  the  want  of  a 
definite  term  for  the  function  power. 

The  term  force  ought  to  be  introduced  into  the  German  and  Scan- 
dinavian languages,  leaving  the  term  kraft  to  denote  power. 


NYSTROM'S  ANSWER  183 

tains  100  cylindrical  gallons.  So  it  should  be  with  designation  of 
work,  not  to  give  different  names  to  the  work  according  to  the  pro- 
portion of  its  constituent  elements. 

It  is  customary  to  distinguish  indoor  work  from  outdoor  work,  but 
in  Dynamics  it  is  all  F  V  T. 

§  36.  There  exists  only  one  kind  of  work  in  Dynamics — namely, 
the  product  of  the  three  simple  physical  elements,  force,  velocity  and 
time. 

I  should  like  you  very  much  to  go  to  a  machine-shop  and  explain 
practically  to  the  workmen,  foremen  and  superintendent  your  nomen- 
clature of  work ;  and  if  you  can  make  them  understand  and  appreciate 
it  without  laughing  at  you,  I  am  very  much  mistaken. 

Heat  is  convertible  into  work,  and  consequently  must  consist  of 
F  V  T,  which  is  actually  the  case.  The  force  F  is  represented  by  the 
temperature  of  the  heat  and  V  T  by  the  space  it  occupies  in  the  gas 
or  vapor. 

§  37.  The  act  of  combustion  is  power,  which  multiplied  by  time  is 
work ;  also,  the  act  of  evaporation  is  power,  which  multiplied  by  time 
is  work ;  but  in  both  cases  the  work  of  the  heat  is  simply  K=F  V  T. 

It  is  immaterial  whether  you  call  it  external,  internal  or  infernal 
work,  it  is  still  K=  F  V  T,  and  nothing  else. 

§  38.  Your  classification  of  work  is  not  accompanied  with  the 
requisite  definitions  to  render  your  argument  admissible. 

§  40.  I  beg  you  to  accept  my  sincere  thanks  for  your  frank  and 
unsparing  remarks  on  my  work.  You  have  liberally  furnished  pre- 
cisely what  I  wanted  and  asked  for  in  order  to  test  the  validity  of 
my  reorganization  of  Dynamics. 

In  discussions  of  this  kind  it  is  necessary  to  be  frank  and  free  the 
mind  from  fiction,  for  otherwise  we  could  not  rightly  understand  one 
another,  and  the  interest  of  science,  which  we  both  have  at  heart, 
would  suffer,  notwithstanding  our  different  and  even  discordant  views. 

In  conclusion  let  me  hope  that  none  of  my  expressions  blynter- 
preted  into  a  want  of  kind  and  courteous  feeling  toward  your  per- 
sonality, and  I  remain,  with  great  consideration, 

Yours  respectfully, 

JOHN  W.  NYSTROM, 

Civil  Engineer. 
1010  Spruce  Street, 
Philadelphia,  Sept.  1,  1875. 


184  MECHANICAL   TERMS. 

In  -the  English  translation  of  Weisbach's  Mechanics,  the  term  and 
function  "  power,"  which  is  one  of  the  most  important  functions  in 
Dynamics,  does  not  appear.  Even  the  term  "horse-power"  is  omitted, 
and  cannot  be  found  in  the  index  of  that  book  which  otherwise 
abounds  in  terms  and  expressions  like  those  of  Professor  Schmidt. 

On  pages  15  and  16  are  given  a  number  of  rejected  terms,  which 
are  considered  superfluous  and  confusing  in  the  language  of  me- 
chanics. 

This  kind  of  terms  are  limited  only  to  books  and  schools,  where  they 
burden  the  student  and  tax  his  time  and  mind  to  no  purpose,  but  only 
to  be  forgotten  when  he  finds  no  equivalent  for  them  in  practice. 

The  crowd  of  subjects  which  engross  the  brief  years  of  a  school 
career  exact  a  severe  economy  of  time  and  labor  by  the  student.  It 
becomes  a  paramount  consideration,  therefore,  that  his  acquirements 
should  in  his  subsequent  experience  be  found  to  possess  an  unequivo- 
cal practical  value,  which  has  heretofore  not  been  fully  realized. 

A  graduated  student  of  Mechanics,  although  expected  to  be  well 
versed  in  that  subject,  is,  when  brought  to  a  practical  test,  often  found 
wanting,  as  is  shown  in  periodicals  of  the  day,  where  we  rarely  find  a 
sound  article  on  Dynamics.  For  example,  in  the  London  Engineer 
lately  appeared  an  article  on  Dynamics  of  heavy  ordnance,  written  by 
an  English  artillery  officer,  stating  that 


W  V ' 
"  The  energy  in  vis  viva  in  pounds  =  — 


IFF2 
whereas  it  is  not  pounds,  but  work  =  — 


This  function  is  called  "energy"  by  doctors  of  philosophy,  who  very 
often  represent  it  as  a  very  mysterious  phenomenon. 

The  term  "  energy  "  is  not  used  in  the  English  translation  of  Wei.<- 
bach,  except  in  a  note  by  the  translator. 

The  term  "  energy "  is  derived  from  the  Greek  tv-fyyou,  of  which 
fv  means  inner  or  within,  and  ipfoo  means  work. 

"  Kinetic  energy  "  (x^ro^-lp^ou}  means  moving  energy. 

"  Potential  energy  "  (Latin,  potentalis)  means  powerful  energy. 

These  terms  and  expressions  have  originated  at  times  when  the 
science  of  Dynamics  was  in  a  very  clouded  condition,  and  have  since 
been  retained  with  various  kinds  of  conflicting  definitions. 


MECHANICAL   TERMS.  185 

The  sense  in  which  the  term  "  energy  "  is  generally  used,  means 
simply  "  work,"  which  consists  of  only  F  V  T,  and  nothing  more  or  less. 

WV1 
In  the  formula ,  V  means  the  final  velocity  of  a  falling  body, 

19 
which  is  double  the  mean  velocity  of  the  fall.    W=  force  of  gravity  F, 

y 
and  T=  — ,  the  time  in  seconds  of  the  fall,  of  which  F=<?  T. 


WV2       WVT 
Energy  or  work,  K=  ^—  =  ULL 

It  is  simply  the  force  F  of  gravity  which  accomplished  the  work  K 
of  the  falling  body,  giving  it  a  velocity  F  in  the  time  T. 

There  exists  no  such  distinction  as  inner  or  outer  energy  or  work, 
nor  kinetic  or  potential  energy,  which  are  all  simply  work  K—FVT. 

When  a  reader  attempts  to  gather  information  from  a  book  with 
those  high-sounding  terms,  he  may  be  impressed  with  the  idea  that 
the  subject  is  much  too  profound  for  him  to  learn,  and  that  he  has 
not  sufficient  intellect  to  grasp  it,  whilst  the  fact  is  that  there  is  noth- 
ing in  it  but  simply  F  V  T. 

One  evil  of  high-sounding  terms  is  that  they  are  often  sophistically 
and  successfully  used  for  delusion,  of  which  the  writer  could  refer  to 
many  cases,  but  fears  that  in  so  doing  his  motives  would  be  misun- 
derstood. 

On  one  occasion  a  professor  whilst  arguing  the  subject  of  radiation 
of  heat  spoke  about  "  dynamical  temperature,  statical  temperature, 
potential  temperature  and  actual  temperature."  On  being  asked 
"What  is  the  difference  between  potential  and  actual  temperatures?" 
the  professor  answered,  "  Potential  temperature  refers  to  volume." 

Question.  "  Is  potential  temperature  measured  by  a  thermometer  ?" 

The  professor  could  not  answer,  but  gave  it  up. 

High-sounding  terms,  in  fact,  serve  the  same  purpose  as  feathers 
of  many  colors  in  a  hat — namely,  to  decorate  the  subject. 


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